Question

Найдите корень уравнения:
1) х^2+3х-(1-2х^2)=3х^2-х+4
2) (х-5)^2+(х+4)^2=2х^2

Answer 1

1.
$x^{2} + 3x-(1- 2x^{2}) = 3x^{2} -x+4$
$x^{2} +3x-1+ 2x^{2} - 3x^{2} +x-4=0$
$x^{2} + 2x^{2} - 3x^{2} +3x+x=1-4$
$4x=-3$
$x=-0,75$

2.
$(x-5)^{2} + (x+4)^{2} = 2x^{2}$
$x^{2} -10x+25+ x^{2} +8x+16- 2x^{2} = 0$
$x^{2} + x^{2} - 2x^{2} -10x+8x=-25+16$
$-10x+8x=-25+16$
$-2x=-9$
$x=4,5$