5^sin^2(x) = √5 =>
![5^{sin^2 (x)}= 5^{1/2} <=> \\ sin^2(x)=1/2 \\(1-cos(2x))/2=1/2 \\ cos(2x)=0 \\ 2x=\pi /2+\pi*k \\ x=\pi /4 + \pi*k/2](https://tex.z-dn.net/?f=5%5E%7Bsin%5E2+%28x%29%7D%3D+5%5E%7B1%2F2%7D+%3C%3D%3E+%5C%5C+sin%5E2%28x%29%3D1%2F2+%5C%5C%281-cos%282x%29%29%2F2%3D1%2F2+%5C%5C+cos%282x%29%3D0+%5C%5C+2x%3D%5Cpi+%2F2%2B%5Cpi%2Ak+%5C%5C+x%3D%5Cpi+%2F4+%2B+%5Cpi%2Ak%2F2+)
Пусть t=√x/x-1, t>0.
t-3/t=1/2, домножим на 2t:
2t^2-t-6=0
D=1+48=49
t1=(1+7)/4=2
t2=(1-7)/4=-3/2<0 - посторонний корень
√x/x-1=2
Возводим в квадрат:
x/(x-1)=4 => x=4x-4 => x=3/4.
2х²-3ху+у²=12
х²-2ху+у² +х²- ху =12
(х²-2ху+у² )+ (х²- ху) =12
(х-у)² +х*(х-у) =12
(х-у)*(х-у+х)=12
(х-у)*( 2х-у)=12
2х-у = 12/(х-у)
-1/5x^2+20=0
1/5x^2-20=0
Умножим каждый член уравнения на "5":
x^2-100=0
(x-10)(x+10)=0
x-10=0 U x+10=0
x=10 U x=-10
Ответ: x=10