1) 5 х²=25 х 2) 100 х²-16=0 3) 3 х²-11 х-4=0 4) х²-3 х+1=0 5) 2 х²+5 х+9=х+2 6) (х-4) (4 х+6) = (х-5) ² 7) 3 х²+6 х/2=4-2 х

Решим уравнения:

1) 5 * х^2 = 25 * х;

5 * x^2 - 25 * x = 0;

5 * x * (x - 5) = 0;

{ x = 0;

x - 5 = 0;

{ x = 0;

x = 5;

2) 100 * х^2 - 16 = 0;

(10 * x) ^2 - 4^2 = 0;

(10 * x + 4) * (10 * x - 4) = 0;

{ 10 * x + 4 = 0;

10 * x - 4 = 0;

{ 10 * x = - 4;

10 * x = 4;

{ x = - 4/10;

x = 4/10;

{ x = - 2/5;

x = 2/5;

3) 3 * х^2 - 11 * х - 4 = 0;

D = 121 + 4 * 3 * 4 = 169;

x1 = (11 + 13) / 6 = 24/6 = 4;

x2 = (11 - 13) / 6 = - 2/6 = - 1/3;

4) х^2 - 3 * х + 1 = 0;

x ₁ = (3 - √ 5) / (2·1) ≈ 0.38197;

x ₂ = (3 + √ 5) / (2·1) ≈ 2.6180;

5) 2 * х^2 + 5 * х + 9 = х + 2;

2 * x^2 + 4 * x + 7 = 0;

D = b ^2 - 4 * a * c = 4 ^2 - 4 · 2 · 7 = 16 - 56 = - 40;

Уравнение не имеет корней.

6) (х - 4) * (4 * х + 6) = (х - 5) ^2;

4 * x^2 + 6 * x - 16 * x - 24 = x^2 - 10 * x + 25;

4 * x^2 - 10 * x - 24 - x^2 + 10 * x - 25 = 0;

3 * x^2 - 24 - 25 = 0;

3 * x^2 - 49 = 0;

x^2 = 49/3;

x = + -7/√3;

7) (3 * х^2 + 6 * х) / 2 = 4 - 2 * х;

3 * x^2 + 6 * x = 8 - 4 * x;

3 * x^2 + 6 * x + 4 * x - 8 = 0;

3 * x^2 + 10 * x - 8 = 0;

x = 2/3 и х = - 4.