Bài 3: Liên hệ giữa phép nhân và phép khai phương
Hướng dẫn giải Bài 23 (Trang 15 SGK Toán 9, Tập 1)
<p><strong>B&agrave;i 23 (Trang 15 SGK To&aacute;n 9, Tập 1):</strong></p> <p>Chứng minh:</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo>&#160;</mo><mfenced><mrow><mn>2</mn><mo>-</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mo>&#160;</mo><mfenced><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>1</mn><mspace linebreak="newline"/><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo>)</mo><mo>&#160;</mo><mo>&#160;</mo><msqrt><mn>2006</mn></msqrt><mo>-</mo><msqrt><mn>2005</mn></msqrt><mo>&#160;</mo><mo>&#160;</mo><mi>v&#224;</mi><mo>&#160;</mo><msqrt><mn>2006</mn></msqrt><mo>+</mo><msqrt><mn>2005</mn></msqrt><mo>&#160;</mo><mi>l&#224;</mi><mo>&#160;</mo><mi>hai</mi><mo>&#160;</mo><mi>s&#7889;</mi><mo>&#160;</mo><mi>ngh&#7883;ch</mi><mo>&#160;</mo><mi>&#273;&#7843;o</mi><mo>&#160;</mo><mi>c&#7911;a</mi><mo>&#160;</mo><mi>nhau</mi><mo>.</mo></math></p> <p>&nbsp;</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>&#160;</mo><mo>&#160;</mo><mfenced><mrow><mn>2</mn><mo>-</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mo>&#160;</mo><mfenced><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mn>2</mn><mn>2</mn></msup><mo>-</mo><msup><mfenced><msqrt><mn>3</mn></msqrt></mfenced><mn>2</mn></msup><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>4</mn><mo>-</mo><mn>3</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>1</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><mfenced><mrow><msqrt><mn>2006</mn></msqrt><mo>-</mo><msqrt><mn>2005</mn></msqrt></mrow></mfenced><mo>&#160;</mo><mfenced><mrow><msqrt><mn>2006</mn></msqrt><mo>+</mo><msqrt><mn>2005</mn></msqrt></mrow></mfenced><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mfenced><msqrt><mn>2006</mn></msqrt></mfenced><mn>2</mn></msup><mo>-</mo><msup><mfenced><msqrt><mn>2005</mn></msqrt></mfenced><mn>2</mn></msup><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>2006</mn><mo>-</mo><mn>2005</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>1</mn><mspace linebreak="newline"/><mspace linebreak="newline"/><mi>V&#7853;y</mi><mo>&#160;</mo><msqrt><mn>2006</mn></msqrt><mo>-</mo><msqrt><mn>2005</mn></msqrt><mo>&#160;</mo><mo>&#160;</mo><mi>v&#224;</mi><mo>&#160;</mo><msqrt><mn>2006</mn></msqrt><mo>+</mo><msqrt><mn>2005</mn></msqrt><mo>&#160;</mo><mi>l&#224;</mi><mo>&#160;</mo><mi>hai</mi><mo>&#160;</mo><mi>s&#7889;</mi><mo>&#160;</mo><mi>ngh&#7883;ch</mi><mo>&#160;</mo><mi>&#273;&#7843;o</mi><mo>&#160;</mo><mi>c&#7911;a</mi><mo>&#160;</mo><mi>nhau</mi><mo>.</mo></math></p>
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