Câu 45 : Trang 20 - toán 8 tập 1 phần đại số
Tìm x, biết:
a) 2 – 25x2 = 0;
b) x2 – x + \(\frac{1}{4}\) = 0
Bài Làm:
a) 2 – 25x2 = 0
<=> ($\sqrt{2}$)2 – (5x)2 = 0
<=> ($\sqrt{2}$– 5x)( $\sqrt{2}$ + 5x) = 0
$\left[ \begin{array}{ll} \sqrt{2} - 5x = 0 \\ \sqrt{2} + 5x = 0 \\\end{array} \right.$
$\Leftrightarrow\left[ \begin{array}{ll} 5x = \sqrt{2} \\ 5x = - \sqrt{2} \\\end{array} \right.$
$\Leftrightarrow \left[ \begin{array}{ll} x = \frac{\sqrt{2}}{5} \\ x = \frac{-\sqrt{2}}{5} \\\end{array} \right.$
b) x2 - x + \(\frac{1}{4}\) = 0
<=> x2 – 2 . x . \(\frac{1}{2}\) + (\(\frac{1}{2}\))2 = 0
<=> (x - \(\frac{1}{2}\))2 = 0
<=> x - \(\frac{1}{2}\) = 0
<=> x = \(\frac{1}{2}\)