Bài 6: Biến đổi đơn giản biểu thức chứa căn thức bậc hai
Hướng dẫn giải Bài 47 (Trang 27 SGK Toán 9, Tập 1)
<p><strong>Bài 47 (Trang 27 SGK Toán 9, Tập 1):</strong></p>
<p>Rút gọn:</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo> </mo><mo> </mo><mfrac><mn>2</mn><mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>-</mo><msup><mi mathvariant="normal">y</mi><mn>2</mn></msup></mrow></mfrac><mo>.</mo><msqrt><mfrac><mrow><mn>3</mn><msup><mfenced><mrow><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi></mrow></mfenced><mn>2</mn></msup></mrow><mn>2</mn></mfrac><mo> </mo><mo> </mo></msqrt><mo> </mo><mi>với</mi><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>≥</mo><mo> </mo><mn>0</mn><mo>,</mo><mo> </mo><mi mathvariant="normal">y</mi><mo> </mo><mo>≥</mo><mo> </mo><mn>0</mn><mo>,</mo><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>≠</mo><mo> </mo><mi mathvariant="normal">y</mi><mo>;</mo><mspace linebreak="newline"/><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo>)</mo><mo> </mo><mo> </mo><mfrac><mn>2</mn><mrow><mn>2</mn><mi mathvariant="normal">a</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>.</mo><msqrt><mn>5</mn><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mfenced><mrow><mn>1</mn><mo>-</mo><mn>4</mn><mi mathvariant="normal">a</mi><mo>+</mo><mn>4</mn><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup></mrow></mfenced></msqrt><mo> </mo><mo> </mo><mi>với</mi><mo> </mo><mi mathvariant="normal">a</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>.</mo></math></p>
<p> </p>
<p><strong><span style="text-decoration: underline;"><em>Hướng dẫn giải:</em></span></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo> </mo><mo> </mo><mfrac><mn>2</mn><mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>-</mo><msup><mi mathvariant="normal">y</mi><mn>2</mn></msup></mrow></mfrac><mo>.</mo><msqrt><mfrac><mrow><mn>3</mn><msup><mfenced><mrow><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi></mrow></mfenced><mn>2</mn></msup></mrow><mn>2</mn></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>2</mn><mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>-</mo><msup><mi mathvariant="normal">y</mi><mn>2</mn></msup></mrow></mfrac><mfenced open="|" close="|"><mrow><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi></mrow></mfenced><msqrt><mfrac><mn>3</mn><mn>2</mn></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mi mathvariant="normal">y</mi></mrow><mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo> </mo><mo>-</mo><mo> </mo><msup><mi mathvariant="normal">y</mi><mn>2</mn></msup></mrow></mfrac><msqrt><msup><mn>2</mn><mn>2</mn></msup><mo>.</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfrac><msqrt><mn>6</mn></msqrt><mrow><mi mathvariant="normal">x</mi><mo>-</mo><mi mathvariant="normal">y</mi></mrow></mfrac><mo> </mo><mfenced><mrow><mi>vì</mi><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>≥</mo><mo> </mo><mn>0</mn><mo>,</mo><mo> </mo><mi mathvariant="normal">y</mi><mo> </mo><mo>≥</mo><mo> </mo><mn>0</mn><mo>,</mo><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>≠</mo><mo> </mo><mi mathvariant="normal">y</mi><mo> </mo><mi>nên</mi><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mi mathvariant="normal">y</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn></mrow></mfenced><mo>.</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>)</mo><mo> </mo><mfrac><mn>2</mn><mrow><mn>2</mn><mi mathvariant="normal">a</mi><mo>-</mo><mn>1</mn></mrow></mfrac><msqrt><mn>5</mn><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mfenced><mrow><mn>1</mn><mo>-</mo><mn>4</mn><mi mathvariant="normal">a</mi><mo>+</mo><mn>4</mn><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup></mrow></mfenced></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>2</mn><mrow><mn>2</mn><mi mathvariant="normal">a</mi><mo>-</mo><mn>1</mn></mrow></mfrac><msqrt><mn>5</mn><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mn>2</mn><mi mathvariant="normal">a</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mfrac><mrow><mn>2</mn><mfenced open="|" close="|"><mi mathvariant="normal">a</mi></mfenced><mo>.</mo><mfenced open="|" close="|"><mrow><mn>1</mn><mo>-</mo><mn>2</mn><mi mathvariant="normal">a</mi></mrow></mfenced><msqrt><mn>5</mn></msqrt></mrow><mrow><mn>2</mn><mi mathvariant="normal">a</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>2</mn><mo>.</mo><mi mathvariant="normal">a</mi><mfenced><mrow><mn>2</mn><mi mathvariant="normal">a</mi><mo>-</mo><mn>1</mn></mrow></mfenced><msqrt><mn>5</mn></msqrt></mrow><mrow><mn>2</mn><mi mathvariant="normal">a</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn><msqrt><mn>5</mn></msqrt><mi mathvariant="normal">a</mi><mspace linebreak="newline"/><mspace linebreak="newline"/><mfenced><mrow><mi>Vì</mi><mo> </mo><mi mathvariant="normal">a</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn><mo>,</mo><mn>5</mn><mo> </mo><mi>nên</mi><mo> </mo><mi mathvariant="normal">a</mi><mo> </mo><mo>></mo><mo> </mo><mn>0</mn><mo> </mo><mo>⇒</mo><mo> </mo><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn><mi mathvariant="normal">a</mi><mo> </mo><mo><</mo><mo> </mo><mn>0</mn></mrow></mfenced></math></p>
Hướng dẫn Giải Bài 47 (trang 27, SGK Toán 9, Tập 1)
GV: 
GV colearn
GV colearn
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Hướng dẫn Giải Bài 47 (trang 27, SGK Toán 9, Tập 1)
GV: GV colearn
GV colearn