Question

решите уравнения
(5у-1) в квадрате -(2у+5)в квадрате =0

Answer 1

(5y-1)²-(2y+5)²=0

25y²-10y+1-(4y²+20y+25)=0

25y²-10y+1-4y²-20y-25=0

21y²-30y-24=0

7y²-10y-8=0

a=7, b=-10, c=-8

D=√{(-10)²-4*7*(-8)}=100+224=324=18²

$y_{1,2}=\frac{10\pm \sqrt{18^2}}{2*7} = \frac{10\pm 18}{14}$

$y_1=\frac{10+18}{14} = \frac{28}{14} = \boxed{2}$

$y_2=\frac{10-18}{14} = \frac{-8}{14} = \boxed{ -\frac{4}{7}}$