1.√x=x-6 2. x+√41-x^2 3.√x-3=x-9 4.√x-1+√2x-1=5 5.√5x-4+√2x-1=√3x+1

1. √x = x - 6;

x = x ^ 2 - 12 * x + 36;

x ^ 2 - 13 * x + 36 = 0;

Найдем дискриминант квадратного уравнения:

D = b ² - 4 ac = (-13) ² - 4·1·36 = 169 - 144 = 25;

Так как дискриминант больше нуля то, квадратное уравнение имеет два действительных корня:

x ₁ = (13 - √ 25) / (2·1) = (13 - 5) / 2 = 8/2 = 4;

x ₂ = (13 + √ 25) / (2·1) = (13 + 5) / 2 = 18/2 = 9;

2. x = √ (41 - x ^ 2);

x ^ 2 = 41 - x ^ 2;

2 * x ^ 2 = 41;

x ^ 2 = 41/2;

x ^ 2 = 20.5;

x = + - 20.5 ^ (1/2);

3. √ (x - 3) = x - 9;

x - 3 = x ^ 2 - 18 * x + 81;

x ^ 2 - 19 * x + 84 = 0;

x = 7;

x = 12;

4. √ (x - 1) + √ (2 * x - 1) = 5;

x - 1 + 2 * √ (x - 1) + √ (2 * x - 1) + 2 * x - 1 = 25;

3 * x - 2 + 2 * √ (x - 1) + √ (2 * x - 1) = 25;

2 * √ (x - 1) + √ (2 * x - 1) = 25 - 3 * x - 2;

2 * √ (x - 1) + √ (2 * x - 1) = 23 - 3 * x;

4 * (x - 1) * (2 * x - 1) = 529 - 138 * x + 9 * x ^ 2;

4 * (2 * x ^ 2 - 3 * x + 1) = 529 - 138 * x + 9 * x ^ 2;

8 * x ^ 2 - 12 * x + 4 = 529 - 138 * x + 9 * x ^ 2;

x ^ 2 - 126 * x + 525 = 0;

x = 63 - 2√ 861;

x = 63 + 2√ 861;

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

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

2 * √ (5 * x - 4) * √ (2 * x - 1) + 7 * x - 5 = 3 * x + 1;

2 * √ (5 * x - 4) * √ (2 * x - 1) = - 4 * x + 6;

4 * (5 * x - 4) * (2 * x - 1) = 36 - 48 * x + 16 * x ^ 2;

4 * (10 * x ^ 2 - 13 * x + 4) = 36 - 48 * x + 16 * x ^ 2;

10 * x ^ 2 - 13 * x + 4 = 9 - 12 * x + 4 * x ^ 2;

6 * x ^ 2 - x - 5 = 0;

x = - 5/6;

x = 1.