Bài 3: Liên hệ giữa phép nhân và phép khai phương
Hướng dẫn giải Bài 24 (Trang 15 SGK Toán 9, Tập 1)
<p><strong>B&agrave;i 24 (Trang 15 SGK To&aacute;n 9, Tập 1):</strong></p> <p>R&uacute;t gọn v&agrave; t&igrave;m gi&aacute; trị (l&agrave;m tr&ograve;n đến chữ số thập ph&acirc;n thứ ba) của c&aacute;c ẩn thức sau:</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>.</mo><msqrt><mn>4</mn><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mn>6</mn><mi mathvariant="normal">x</mi><mo>+</mo><mn>9</mn><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup></mrow></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mi>t&#7841;i</mi><mo>&#160;</mo><mi mathvariant="normal">x</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><msqrt><mn>2</mn></msqrt><mspace linebreak="newline"/><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo>.</mo><mo>&#160;</mo><msqrt><mn>9</mn><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mfenced><mrow><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>-</mo><mn>4</mn><mi mathvariant="normal">b</mi></mrow></mfenced></msqrt><mo>&#160;</mo><mo>&#160;</mo><mi>t&#7841;i</mi><mo>&#160;</mo><mi mathvariant="normal">a</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>&#160;</mo><mi mathvariant="normal">b</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><msqrt><mn>3</mn></msqrt></math></p> <p>&nbsp;</p> <p><strong><span style="text-decoration: underline;"><em>Hướng dẫn giải:</em></span></strong></p> <p><strong><span style="text-decoration: underline;"><em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo>&#160;</mo><msqrt><mn>4</mn><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mn>6</mn><mi mathvariant="normal">x</mi><mo>+</mo><mn>9</mn><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup></mrow></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><mn>4</mn><msup><mfenced open="|" close="|"><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mn>3</mn><mi mathvariant="normal">x</mi></mrow></mfenced><mn>2</mn></msup></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><mn>4</mn></msqrt><mo>.</mo><msqrt><msup><mfenced open="|" close="|"><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mn>3</mn><mi mathvariant="normal">x</mi></mrow></mfenced><mn>2</mn></msup></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>2</mn><mfenced open="|" close="|"><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mn>3</mn><mi mathvariant="normal">x</mi></mrow></mfenced><mn>2</mn></msup></mfenced><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>2</mn><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mn>3</mn><mi mathvariant="normal">x</mi></mrow></mfenced><mn>2</mn></msup><mo>&#160;</mo><mo>(</mo><mi>v&#236;</mi><mo>&#160;</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mn>3</mn><mi mathvariant="normal">x</mi></mrow></mfenced><mn>2</mn></msup><mo>&#160;</mo><mo>&#8805;</mo><mo>&#160;</mo><mn>0</mn><mo>)</mo></math></em></span></strong></p> <p>Gi&aacute; trị của biểu thức tại <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo>=</mo><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>&#160;</mo><mi>l&#224;</mi><mo>&#160;</mo><mn>2</mn><mfenced open="|" close="|"><mrow><mn>1</mn><mo>+</mo><mn>3</mn><msup><mfenced><mrow><mo>-</mo><msqrt><mn>2</mn></msqrt></mrow></mfenced><mn>2</mn></msup></mrow></mfenced><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>&#160;</mo><mn>2</mn><msup><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mn>3</mn><msqrt><mn>2</mn></msqrt><mo>)</mo></mrow><mn>2</mn></msup><mo>&#160;</mo><mo>&#8776;</mo><mo>&#160;</mo><mn>21</mn><mo>,</mo><mn>029</mn><mo>.</mo></math></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>)</mo><mo>&#160;</mo><msqrt><mn>9</mn><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mfenced><mrow><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>-</mo><mn>4</mn><mi mathvariant="normal">b</mi></mrow></mfenced></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><msup><mfenced><mrow><mn>3</mn><mi mathvariant="normal">a</mi></mrow></mfenced><mn>2</mn></msup><msup><mfenced><mrow><mi mathvariant="normal">b</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><msup><mfenced><mrow><mn>3</mn><mi mathvariant="normal">a</mi></mrow></mfenced><mn>2</mn></msup></msqrt><msqrt><msup><mfenced><mrow><mi mathvariant="normal">b</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfenced open="|" close="|"><mrow><mn>3</mn><mi mathvariant="normal">a</mi></mrow></mfenced><mo>.</mo><mfenced open="|" close="|"><mrow><mi mathvariant="normal">b</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></p> <p>Gi&aacute; trị của biểu thức tại<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#160;</mo><mi mathvariant="normal">a</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>&#160;</mo><mi mathvariant="normal">b</mi><mo>=</mo><mo>-</mo><msqrt><mn>3</mn></msqrt><mo>&#160;</mo><mi>l&#224;</mi><mo>&#160;</mo><mfenced open="|" close="|"><mrow><mn>3</mn><mo>.</mo><mfenced><mrow><mo>-</mo><mn>2</mn></mrow></mfenced></mrow></mfenced><mo>.</mo><mfenced open="|" close="|"><mrow><mo>-</mo><msqrt><mn>3</mn></msqrt><mo>-</mo><mn>2</mn></mrow></mfenced><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>6</mn><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>2</mn></mrow></mfenced><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>6</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>12</mn><mo>&#160;</mo><mo>&#8776;</mo><mo>&#160;</mo><mn>22</mn><mo>,</mo><mn>392</mn><mo>.</mo></math></p>
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