X^2 - x - y^2 - y = x^2 - y^2 - x - y = (x - y)(x + y) - 1(x + y) = (x + y) (x - y - 1)
<span>(5sinx - 12cosx)^2 = 13^2
</span>25sin^2x - 120sinxcosx + 144cos^2x = 169sin^2x + 169cos^2x
- 144sin^2x - 120sinxcosx - 25cos^2x = 0 /:(-1)
144sin^2x + 120sincosx + 25cos^2x = 0
(12 sinx + 5cosx)^2 = 0
12sinx + 5cosx = 0 /:cosx ≠ 0
12tgx + 5 = 0
12tgx = - 5
tgx = - 5/12
x = - arctg(5/12) + pik, k ∈Z
7z*(x-y)-5*(y-x)=7z*(x-y)-5*(-(x-y))=7z*(x-y)+5(x-y)=(x-y)*(7z+5)