Question

Решите уравнение
a) 1/4x^2=0,16
b) x^3-4x^2-x+4=0

Answer 1

а)

$\displaystyle \tt \frac{1}{4}x^2=0,16 \: \: \: \: | \cdot 4\\\displaystyle \tt x^2=0,64\\\displaystyle \tt x=\sqrt{0,64}\\\displaystyle \tt x_1=0,8\\\displaystyle \tt x=-\sqrt{0,64}\\\displaystyle \tt x_2=-8$

б)

$\displaystyle \tt x^3-4x^2-x+4=0\\\displaystyle \tt x^2(x-4)-(x-4)=0\\\displaystyle \tt (x-4)(x^2-1)=0\\\displaystyle \tt x-4=0\\\displaystyle \tt x_1=4\\\displaystyle \tt x^2-1=0\\\displaystyle \tt x^2=1\\\displaystyle \tt x=\sqrt{1}\\\displaystyle \tt x_2=1\\\displaystyle \tt x=-\sqrt{1}\\\displaystyle \tt x_3=-1$