Найдите корни уравнения: 1) (х-1)^2=29-5x; 2) 5(x-2)=(3x+2)(x-2); 3) (x^2+2x)/2=(x^2+24)/7

Question

Найдите корни уравнения:
1) (х-1)^2=29-5x;

2) 5(x-2)=(3x+2)(x-2);

3) (x^2+2x)/2=(x^2+24)/7

Answer 1

X^2 - 2x + 1 = 29 - 5x
x^2 + 3x - 28 =0
D = b^2 - 4ac = 9 + 112 = 121 = 11^2
x1 = ( - 3 + 11) / 2 = 4
x2 = ( - 3 - 11) / 2 = - 7

5x - 10 = 3x^2 - 4x - 4
- 3x^2 + 9x - 6 = 0
x^2 - 3x + 2 = 0
D = b^2 - 4ac = 9 - 8 = 1
x1 = ( 3 + 1)/2 = 2
x2 = ( 3 - 1) / 2 = 1

7(x^2 + 2x) = 2( x^2 + 24)
7x^2 + 14x = 2x^2 + 48
7x^2 - 2x^2 + 14x - 48 = 0
5x^2 + 14x - 48 = 0
D = b^2 - 4ac = 196 + 960 = 1156 = 34^2
x1 = ( - 14 + 34) / 10 = 2
x2 = ( - 14 - 34) / 10 = - 4,8