sqrt(3x-5)-4=5sqrt(3x-5) = 93x - 5 = 813x = 86x = 86/3 = 28.666
sqrt(x^2-3x-1+7)=2xsqrt(x^2-3x+6) = 2xx^2 - 3x + 6 = 4x^23x = -6x = -2
x-sqrt(25-x^2) = 7sqrt(25-x^2) = x - 725 - x^2 = x^2 - 14x + 492x^2 - 14x - 24 = 0x^2 - 7x - 12 = 0(x - 4)(x - 3) = 0x = 4 or x = 3
sqrt(2x-1)=x-22x - 1 = x^2 - 4x + 4x^2 - 6x + 5 = 0(x - 5)(x - 1) = 0x = 5 or x = 1
3+sqrt(3x+1)=xsqrt(3x + 1) = x - 33x + 1 = x^2 - 6x + 9x^2 - 9x + 8 = 0(x - 8)(x - 1) = 0x = 8 or x = 1
Итак, решения иррациональных уравнений:
sqrt(3x-5)-4=5
sqrt(3x-5) = 9
3x - 5 = 81
3x = 86
x = 86/3 = 28.666
sqrt(x^2-3x-1+7)=2x
sqrt(x^2-3x+6) = 2x
x^2 - 3x + 6 = 4x^2
3x = -6
x = -2
x-sqrt(25-x^2) = 7
sqrt(25-x^2) = x - 7
25 - x^2 = x^2 - 14x + 49
2x^2 - 14x - 24 = 0
x^2 - 7x - 12 = 0
(x - 4)(x - 3) = 0
x = 4 or x = 3
sqrt(2x-1)=x-2
2x - 1 = x^2 - 4x + 4
x^2 - 6x + 5 = 0
(x - 5)(x - 1) = 0
x = 5 or x = 1
3+sqrt(3x+1)=x
sqrt(3x + 1) = x - 3
3x + 1 = x^2 - 6x + 9
x^2 - 9x + 8 = 0
(x - 8)(x - 1) = 0
x = 8 or x = 1
Итак, решения иррациональных уравнений:
x = 28.666x = -2x = 4 or x = 3x = 5 or x = 1x = 8 or x = 1