1) / sqrt{x+3}+/sqrt{3x-3}=10 2) 2-/sqrt{5x}+/sqrt{2x-1}=0 3) 5+/{x/^{2}+x+7}=2x

Вычислим корни уравнений.

1) √ (x + 3) + √ (3 * x - 3) = 10;

Возведем в квадрат.

x + 3 + √ (x + 3) * √ (3 * x - 3) + 3 * x - 3 = 100;

√ (x + 3) * √ (3 * x - 3) + 4 * x = 100;

√ (x + 3) * √ (3 * x - 3) = 100 - 4 * x;

(x + 3) * (3 * x - 3) = (100 - 4 * x) ^2;

3 * x^2 - 3 * x + 9 * x - 9 = 10 000 - 800 * x + 16 * x^2;

Упростим.

13 * x^2 - 806 * x + 10 009 = 0;

x1 = 31 - 6/1 * 3√897;

x2 = 31 + 6/1 * 3√897.

2) 2 - √ (5 * x) + √ (2 * x - 1) = 0;

2 + √ (2 * x - 1) = √ (5 * x);

Возведем в квадрат.

4 + 2 * 2 * √ (2 * x - 1) + 2 * x - 1 = 5 * x;

4 * √ (2 * x - 1) + 2 * x + 3 = 5 * x;

4 * √ (2 * x - 1) = 5 * x - 2 * x - 3;

4 * √ (2 * x - 1) = 3 * x - 3;

16 * (2 * x - 1) = 9 * x^2 - 18 * x + 9;

32 * x - 16 = 9 * x^2 - 18 * x + 9;

9 * x^2 - 18 * x - 32 * x + 9 + 16 = 0;

9 * x^2 - 40 * x + 25 = 0;

D = 1600 - 4 * 9 * 25 = 700;

x1 = (40 + 10√7) / 18;

x2 = (40 - 10√7) / 18.

3) 5 + √ (x^2 + x + 7) = 2 * x;

x^2 + x + 7 = (2 * x - 5) ^2;

x^2 + x + 7 = 4 * x^2 - 20 * x + 25;

3 * x^2 - 21 * x + 18 = 0;

x^2 - 7 * x + 6 = 0;

D = 49 - 4 * 1 * 6 = 5^2;

x1 = (7 + 5) / 2 = 12/2 = 6;

x2 = (7 - 5) / 2 = 2/2 = 1.