Question

Х² - 6х+4=0. Найдите х1 и х2

Answer 1

X1= 3+√5

X2= 3-√5

$x {}^{2} - 6x + 4 = 0$

По формуле дискриминанта:

$x = \frac{ - b + - \sqrt{b {}^{2} - 4ac} }{2a}$

a= 1; b= -6; c= 4

$x = \frac{ - ( - 6) + - \sqrt{( - 6) {}^{2} - 4 \times 1 \times 4} }{2 \times 1}$

$x = \frac{ 6 + - \sqrt{36 - 16} }{2}$

$x = \frac{6 + - \sqrt{20} }{2}$

$x1 = \frac{6 + 2 \sqrt{5} }{2} = \frac{2(3 + \sqrt{5}) }{2} = 3 + \sqrt{5}$

$x2 = \frac{6 - 2 \sqrt{5} }{2} = \frac{2(3 - \sqrt{5}) }{2} = 3 - \sqrt{5}$