Bài 4: Công thức nghiệm của phương trình bậc hai
Hướng dẫn giải Bài 16 (Trang 45 SGK Toán Đại số 9, Tập 2)
<p>D&ugrave;ng c&ocirc;ng thức nghiệm của phương tr&igrave;nh bậc hai để giải c&aacute;c phương tr&igrave;nh sau :</p> <p>a)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>7</mn><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>3</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn></math>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;b)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>5</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn></math></p> <p>c) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mi>x</mi><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>5</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn></math>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;d) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>5</mn><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn></math></p> <p>e)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>y</mi><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>8</mn><mi>y</mi><mo>&#160;</mo><mo>+</mo><mn>16</mn><mo>=</mo><mo>&#160;</mo><mn>0</mn></math>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;f)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><msup><mi>z</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>24</mn><mi>z</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>9</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn></math></p> <p>&nbsp;<strong>Giải</strong></p> <p>a)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mo>&#160;</mo><mn>7</mn><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>3</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mi>c</mi><mi>&#243;</mi><mo>&#160;</mo><mi>a</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>2</mn><mo>,</mo><mo>&#160;</mo><mi>b</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mn>7</mn><mo>,</mo><mo>&#160;</mo><mi>c</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>3</mn></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#8710;</mo><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mrow><mo>(</mo><mo>-</mo><mn>7</mn><mo>)</mo></mrow><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><mo>.</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>49</mn><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>24</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>25</mn><mo>,</mo><mo>&#160;</mo><msqrt><mo>&#8710;</mo></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>5</mn></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mrow><mo>-</mo><mfenced><mrow><mo>-</mo><mn>7</mn></mrow></mfenced><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>5</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>2</mn></mrow></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>;</mo><mo>&#160;</mo><msub><mi>x</mi><mn>2</mn></msub><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mrow><mo>-</mo><mfenced><mrow><mo>-</mo><mn>7</mn></mrow></mfenced><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>5</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>2</mn></mrow></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>12</mn><mn>4</mn></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>3</mn><mo>&#160;</mo></math></p> <p>b)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>5</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo><mi>c</mi><mi>&#243;</mi><mo>&#160;</mo><mi>a</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>6</mn><mo>,</mo><mo>&#160;</mo><mi>b</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>1</mn><mo>,</mo><mo>&#160;</mo><mi>c</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>5</mn></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#8710;</mo><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mn>1</mn><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><mo>.</mo><mn>6</mn><mo>.</mo><mn>5</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mn>119</mn><mo>:</mo></math> Phương tr&igrave;nh v&ocirc; nghiệm.</p> <p>c)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mi>x</mi><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>5</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo><mi>c</mi><mi>&#243;</mi><mo>&#160;</mo><mi>a</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>6</mn><mo>,</mo><mo>&#160;</mo><mi>b</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>1</mn><mo>,</mo><mo>&#160;</mo><mi>c</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mn>5</mn></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#8710;</mo><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mn>1</mn><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><mo>.</mo><mn>6</mn><mo>.</mo><mfenced><mrow><mo>-</mo><mn>5</mn></mrow></mfenced><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>121</mn><mo>,</mo><mo>&#160;</mo><msqrt><mo>&#8710;</mo></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>11</mn></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mrow><mo>-</mo><mn>1</mn><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>11</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>6</mn></mrow></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mn>1</mn><mo>;</mo><mo>&#160;</mo><msub><mi>x</mi><mn>2</mn></msub><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mrow><mo>-</mo><mn>1</mn><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>11</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>6</mn></mrow></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>&#160;</mo></math></p> <p>d) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>5</mn><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo><mi>c</mi><mi>&#243;</mi><mo>&#160;</mo><mi>a</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>3</mn><mo>,</mo><mo>&#160;</mo><mi>b</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>5</mn><mo>,</mo><mo>&#160;</mo><mi>c</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>2</mn></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#8710;</mo><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mn>5</mn><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><mo>.</mo><mn>3</mn><mo>.</mo><mn>2</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>25</mn><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>24</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>1</mn><mo>,</mo><mo>&#160;</mo><msqrt><mo>&#8710;</mo></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>1</mn></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mrow><mo>-</mo><mn>5</mn><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>1</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>3</mn></mrow></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mn>1</mn><mo>;</mo><mo>&#160;</mo><msub><mi>x</mi><mn>2</mn></msub><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mrow><mo>-</mo><mn>5</mn><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>1</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>3</mn></mrow></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>&#160;</mo></math></p> <p>e)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>y</mi><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>8</mn><mi>y</mi><mo>&#160;</mo><mo>+</mo><mn>16</mn><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mi>c</mi><mi>&#243;</mi><mo>&#160;</mo><mi>a</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>1</mn><mo>,</mo><mo>&#160;</mo><mi>b</mi><mo>=</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>&#160;</mo><mi>c</mi><mo>&#160;</mo><mo>=</mo><mn>16</mn></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#8710;</mo><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mfenced><mrow><mo>-</mo><mn>8</mn></mrow></mfenced><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>16</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>y</mi><mrow><mn>1</mn><mo>&#160;</mo></mrow></msub><mo>=</mo><mo>&#160;</mo><msub><mi>y</mi><mn>2</mn></msub><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mrow><mo>-</mo><mn>8</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>1</mn></mrow></mfrac><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>4</mn></math></p> <p>f)&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><msup><mi>z</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>24</mn><mi>z</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>9</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo><mi>c</mi><mi>&#243;</mi><mo>&#160;</mo><mi>a</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>16</mn><mo>,</mo><mo>&#160;</mo><mi>b</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>24</mn><mo>,</mo><mo>&#160;</mo><mi>c</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>9</mn></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#8710;</mo><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mn>24</mn><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><mo>.</mo><mn>16</mn><mo>.</mo><mn>9</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>z</mi><mrow><mn>1</mn><mo>&#160;</mo></mrow></msub><mo>=</mo><msub><mi>z</mi><mn>2</mn></msub><mo>=</mo><mo>-</mo><mfrac><mn>24</mn><mrow><mn>2</mn><mo>.</mo><mn>16</mn></mrow></mfrac><mo>=</mo><mo>&#160;</mo><mo>-</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></math></p> <p>&nbsp;</p> <p>&nbsp;</p>
Xem lời giải bài tập khác cùng bài