Hướng dẫn giải Bài 52 (Trang 24 SGK Toán Đại số 8, Tập 1)

Chứng minh rằng <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mo>(</mo><mn>5</mn><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></msup><mo>−</mo><mn>4</mn></math> chia hết cho 5 với mọi số nguyên n. Giải: Ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mo>(</mo><mn>5</mn><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></msup><mo>−</mo><mn>4</mn><mo> </mo><mspace linebreak="newline"/><mo>=</mo><msup><mrow><mo>(</mo><mn>5</mn><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></msup><mo>−</mo><msup><mn>2</mn><mn>2</mn></msup><mspace linebreak="newline"/><mo> </mo><mo>=</mo><mo>(</mo><mn>5</mn><mi>n</mi><mo>+</mo><mn>2</mn><mo>−</mo><mn>2</mn><mo>)</mo><mo>(</mo><mn>5</mn><mi>n</mi><mo>+</mo><mn>2</mn><mo>+</mo><mn>2</mn><mo>)</mo><mspace linebreak="newline"/><mo>=</mo><mn>5</mn><mi>n</mi><mo>(</mo><mn>5</mn><mi>n</mi><mo>+</mo><mn>4</mn><mo>)</mo></math> Vì 5 <img id="equationview" title="This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program." src="http://latex.codecogs.com/gif.latex?%5Cvdots" alt="" /> 5 nên 5n(5n + 4) <img id="equationview" title="This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program." src="http://latex.codecogs.com/gif.latex?%5Cvdots" alt="" /> 5 ∀n ∈ Z.