Question

Решить уравнение:
(2х - 1) (2х + 1) + х (х - 1) = 2х (х + 1)

Answer 1

$(2x - 1) (2x + 1) + x (x - 1) = 2x (x + 1)$

$left( 2 x-1 right) left( 2 x+1 right) +x left( x-1 right) -2 x left( x+1 right) = 0$

$4 x^2+2 x-2 x-1+x^2+x left( -1 right) -2 x^2-2 x= 0$

$3 x^2-3 x-1 = 0$ 

$x_{1,2}= frac{-bpmsqrt{D}}{2a} = frac{3pmsqrt{21}}{6} = frac{3pmsqrt{21}}{6}$

$x_1 = frac{3+sqrt{21}}{6},; x_2 = frac{3-sqrt{21}}{6}$

Answer 2

4X^2 - 1 + X^2 - X = 2X^2 + 2X 
5X^2 - 2X^2 - X - 2X - 1 = 0
3X^2 - 3X - 1 = 0
D = 9 -4*3*(-1) = 9 + 12 = 21 
X1 = ( 3 + V 21 ) 6 
X2 = ( 3 - V 21 ) 6