Bài 3: Liên hệ giữa phép nhân và phép khai phương
Hướng dẫn giải Bài 19 (Trang 15 SGK Toán 9, Tập 1)
<p><strong>B&agrave;i 19 (Trang 15 SGK To&aacute;n 9, Tập 1):</strong></p> <p>R&uacute;t gọn c&aacute;c biểu thức sau:</p> <p>&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo>&#160;</mo><msqrt><mn>0</mn><mo>,</mo><mn>36</mn><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup></msqrt><mo>&#160;</mo><mi>v&#7899;i</mi><mo>&#160;</mo><mi mathvariant="normal">a</mi><mo>&#60;</mo><mn>0</mn><mo>;</mo><mspace linebreak="newline"/><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo>)</mo><mo>&#160;</mo><msqrt><msup><mi mathvariant="normal">a</mi><mn>4</mn></msup><msup><mfenced><mrow><mn>3</mn><mo>-</mo><mi mathvariant="normal">a</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mi>v&#7899;i</mi><mo>&#160;</mo><mi mathvariant="normal">a</mi><mo>&#8805;</mo><mn>3</mn><mo>;</mo><mspace linebreak="newline"/><mspace linebreak="newline"/><mi mathvariant="normal">c</mi><mo>)</mo><mo>&#160;</mo><msqrt><mn>27</mn><mo>.</mo><mn>48</mn><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi mathvariant="normal">a</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mi>v&#7899;i</mi><mo>&#160;</mo><mi mathvariant="normal">a</mi><mo>&#62;</mo><mn>1</mn><mo>;</mo><mspace linebreak="newline"/><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#160;</mo><mfrac><mn>1</mn><mrow><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfrac><msqrt><msup><mi mathvariant="normal">a</mi><mn>4</mn></msup><msup><mfenced><mrow><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mi>v&#7899;i</mi><mo>&#160;</mo><mi mathvariant="normal">a</mi><mo>&#62;</mo><mi mathvariant="normal">b</mi><mspace linebreak="newline"/></math></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><msqrt><mn>0</mn><mo>,</mo><mn>36</mn><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><msqrt><mn>0</mn><mo>,</mo><mn>36</mn></msqrt><mo>.</mo><msqrt><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>0</mn><mo>,</mo><mn>6</mn><mo>.</mo><mfenced open="|" close="|"><mi mathvariant="normal">a</mi></mfenced><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mn>0</mn><mo>,</mo><mn>6</mn><mi mathvariant="normal">a</mi><mo>&#160;</mo><mo>&#160;</mo><mo>(</mo><mi>v&#236;</mi><mo>&#160;</mo><mi mathvariant="normal">a</mi><mo>&#60;</mo><mn>0</mn><mo>)</mo></math></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>)</mo><mo>&#160;</mo><msqrt><msup><mi>a</mi><mn>4</mn></msup><msup><mfenced><mrow><mn>3</mn><mo>-</mo><mi>a</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><msup><mi>a</mi><mn>4</mn></msup></msqrt><mo>.</mo><msqrt><msup><mfenced><mrow><mn>3</mn><mo>-</mo><mi>a</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfenced open="|" close="|"><msup><mi>a</mi><mn>2</mn></msup></mfenced><mo>.</mo><mfenced open="|" close="|"><mrow><mn>3</mn><mo>-</mo><mi>a</mi></mrow></mfenced><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mi>a</mi><mn>2</mn></msup><mfenced><mrow><mi>a</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>&#160;</mo><mo>(</mo><mi>v</mi><mi>&#236;</mi><mo>&#160;</mo><mi>a</mi><mo>&#8805;</mo><mn>3</mn><mo>&#160;</mo><mi>n</mi><mi>&#234;</mi><mi>n</mi><mo>&#160;</mo><mi>a</mi><mo>-</mo><mn>3</mn><mo>&#160;</mo><mo>&#8805;</mo><mo>&#160;</mo><mn>0</mn><mo>)</mo></math></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">c</mi><mo>.</mo><mo>&#160;</mo><msqrt><mn>27</mn><mo>.</mo><mn>48</mn><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi mathvariant="normal">a</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><msup><mn>9</mn><mn>2</mn></msup><mo>.</mo><msup><mn>4</mn><mn>2</mn></msup><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi mathvariant="normal">a</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><msup><mn>9</mn><mn>2</mn></msup></msqrt><mo>.</mo><msqrt><msup><mn>4</mn><mn>2</mn></msup></msqrt><mo>.</mo><msqrt><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi mathvariant="normal">a</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>9</mn><mo>.</mo><mn>4</mn><mo>.</mo><mfenced open="|" close="|"><mrow><mn>1</mn><mo>-</mo><mi mathvariant="normal">a</mi></mrow></mfenced><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>36</mn><mo>.</mo><mfenced><mrow><mn>1</mn><mo>-</mo><mi mathvariant="normal">a</mi></mrow></mfenced><mo>&#160;</mo><mo>&#160;</mo><mo>(</mo><mi>v&#236;</mi><mo>&#160;</mo><mi mathvariant="normal">a</mi><mo>&#62;</mo><mn>1</mn><mo>&#160;</mo><mi>n&#234;n</mi><mo>&#160;</mo><mn>1</mn><mo>-</mo><mi mathvariant="normal">a</mi><mo>&#60;</mo><mn>0</mn><mo>)</mo></math></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#160;</mo><mfrac><mn>1</mn><mrow><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfrac><msqrt><msup><mi mathvariant="normal">a</mi><mn>4</mn></msup><msup><mfenced><mrow><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>1</mn><mrow><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfrac><mo>.</mo><msqrt><msup><mi mathvariant="normal">a</mi><mn>4</mn></msup></msqrt><mo>.</mo><msqrt><msup><mfenced><mrow><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfenced><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mfrac><mn>1</mn><mrow><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfrac><mo>.</mo><mfenced open="|" close="|"><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup></mfenced><mo>.</mo><mfenced open="|" close="|"><mrow><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfenced><mspace linebreak="newline"/><mspace linebreak="newline"/><mo>=</mo><mo>&#160;</mo><mfrac><mn>1</mn><mrow><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfrac><mo>.</mo><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mo>.</mo><mo>(</mo><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">b</mi><mo>)</mo><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mo>&#160;</mo><mo>&#160;</mo><mo>(</mo><mo>&#160;</mo><mi>v&#236;</mi><mo>&#160;</mo><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mo>&#8805;</mo><mn>0</mn><mo>&#8658;</mo><mo>&#160;</mo><mi mathvariant="normal">a</mi><mo>&#62;</mo><mi mathvariant="normal">b</mi><mo>&#8660;</mo><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">b</mi><mo>&#62;</mo><mn>0</mn><mo>)</mo></math></p>
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