Question

sqrt(5x-4)+sqrt(2x-1)=(sqrt3x+1)

Answer 1

$sqrt{5x-4} + sqrt{2x-1} = sqrt{3x+1}$
5x+4 + 2*$sqrt{(5x-4)(2x-1)}$ + 2x - 1 =3x+1
2*$sqrt{(5x-4)(2x-1)}$ = 6-4x
4 (5x-4)(2x-1) = 36 - 48x + 16x²
40x² - 20x - 32x + 16 - 36 + 48x - 16x² = 0
24x² - 4x - 20 = 0
6x² - x - 5 =0
6 - 1 -5=0
x₁ = 1     
x₂ = -5/6  не удов., т.к. 5x-1≥0
Ответ: 1