Question

Разложить на множители 1)2х^2+3ху-2у^2
2)х^4+4

Answer 1

1)
$2 x^{2} +3xy-2y^2=2(x-0.5y)(x+2y)=(2x-y)(x+2y)$

$2x^2+3xy-2y^2=0$

$a=2$

$b=3y$

$c=-2y^2$

$D=(3y)^2-4*2*(-2y^2)=25y^2$

$x_1= frac{-3y+5y}{4}=0.5y$

$x_2= frac{-3y-5y}{4}=-2y$

2)

$x^4+4= (x^{2} )^{2} +2^2+2*2*x^2-2*2*x^2=( (x^{2} )^{2}+2^2+4x^2)-4x^2=$$=(x^2+2)^2-(2x)^2=(x^2+2+2x)(x^2+2-2x)$