Question

X² -2x-1=0
розв'язати рівняння
даю 15 балів​

Answer 1

$x^{2} -2x-1=0\\\\D=(-2)^{2}-4*(-1)=4+4=8=(2\sqrt{2})^{2}\\\\x_{1}=\frac{2-2\sqrt{2}}{2}=1-\sqrt{2}\\\\x_{2}=\frac{2+2\sqrt{2}}{2}=1+\sqrt{2}$

Answer 2

$\displaystyle x^2 - 2x - 1 = 0 \\\\ \displaystyle D = (-2)^2 - 4 * 1 * (-1) = 4+4 = 8 \\\\ \displaystyle x_1 = \frac{2 + \sqrt8}{2} = \frac{2 + 2\sqrt2}{2} = 1+\sqrt2 \\\\ \displaystyle x_2 = \frac{2 - \sqrt8}{2} = \frac{2 - 2\sqrt2}{2} = 1-\sqrt2$