Question

решите уравнение:
$sqrt{5 - 2x} + sqrt{x - 1} = 2$

Answer 1

$sqrt{5-2x}+sqrt{x-1}=2 \ \ sqrt{5-2x}=2-sqrt{x-1} \ \ left(sqrt{5-2x}right)^2=left(2-sqrt{x-1}right)^2 \ \ 5-2x=x+3-4sqrt{x-1} \ \ -3x+2=-4sqrt{x-1} \ \ left(-3x+2right)^2=left(-4sqrt{x-1}right)^2 \ \ 9x^2-12x+4=16x-16 \ \ 9x^2-12x+20=16x \ \ 9x^2-28x+20=0 \ \ x=frac{-left(-28right)+sqrt{left(-28right)^2-4cdot :9cdot :20}}{2cdot :9} \ \ x= frac{28+sqrt{left(-28right)^2-4cdot :9cdot :20}}{18} \ \ x= frac{28 б sqrt{784-720}}{18}$
$\ \ x=frac{28 б sqrt{64}}{18} \ \ x=frac{28+8}{18} \ \ x=2 \ x=10/9$