Question

1.(х-9)^2=(х-3)^2
2.(х+3)^2+(х-7)^2=2х^2
3.х^2-4х+35=-9х^2+11х+45

Answer 1

$(x-9)^2=(x-3)^2$
$(x-9)(x-9)=(x-3)(x-3)$
$x^2-18x+81=x^2-6x+9$
$x^2-x^2-18x+6x=-81+9$
$-12x=-72$
$x=6$

$(x+3)^2+(x-7)^2=2x^2$
$(x+3)(x+3)+(x-7)(x-7)=2x^2$
$x^2+6x+9-x^2-14x+49=2x^2$
$2x^2+8x=-9-49$
$2x^2+8x=-58$
$2x(x+4)=-58$
$x+4=-58$
$x=-62$

$x^2-4x+35=-9x^2+11x+45$
$x^2-4x+9x^2-11x=-35+45$
$10x^2-15x=10$
$5x(2x-3)=10$
$2x-3=10$
$2x=13$
$x=6.5$