ОДЗ: х ≥ 4/5
√(5x-4) + √(2x-1) = √(3x+1)
5x - 4 + 2x - 1 + 2√((5x-4)(2x-1)) = 3x + 1
4x - 6 + 2√(10x² - 13x + 4) = 0
√(10x² - 13x + 4) = 3 - 2x
10x² - 13x + 4 = 9 - 12x + 4x²
6x² - x - 5 = 0
D = 1 + 120 = 121 = 11²
x1 = (1 - 11)/12 = -10/12 = -5/6 - не подходит
x2 = (1 + 11)/12 = 1
Ответ: 1