2,5n в 4 степени-5n в 2 степени-20=0 (2х-7)2-11(2х-7)+30=0 9(9-5х)2+17(9-5х)+8=0

Для решения уравнения будем использовать замену:

1) 2,5n^4 -5n^2 - 20 = 0.

Пускай n^2 = t:

2,5t^2 - 5t - 20 = 0;

D = b^2 - 4ac = 25 + 200 = 225.

t1 = (-b + √D)/2a = (5 + 15)/5 = 20/5 = 4;

t2 = (-b - √D)/2a = (5 - 15)/5 = -10/5 = -2.

Вернёмся к замене:

n^2 = 4;

n = ±2;

n^2 = -2.

Уравнение не имеет действительных корней.

Ответ: n = ±2.

2) (2x- 7)^2 - 11(2x - 7) + 30 = 0.

Пускай (2х - 7) = t:

t^2 - 11t + 30 = 0;

D = b^2 - 4ac = 121 - 120 = 1;

t1 = (11 + 1)/2 = 12/2 = 6;

t2 = (11 - 1)/2 = 10/2 = 5.

2x - 7 = 6

2x = 13;

x = 6,5.

2x - 7 = 5;

2x = 12;

x = 6.

Ответ: х1 = 6,5, х2 = 6.

3) 9(9 - 5х)^2 + 17(9 - 5х) + 8 = 0.

Пускай 9 - 5х = t:

9t^2 + 17t + 8 = 0;

D = 289 - 288 = 1;

t1 = (-17 + 1)/18 = -16/18 = -8/9;

t2 = (-17 - 1)/18 = -1.

9 - 5x = -8/9;

-5x = -9 8/9;

x = 89/9 : 5;

x = 89/45;

x = 1 44/45.

9 - 5x = -1;

-5x = -10;

x = 2.

Ответ: х1 = 1 44/45, х2 = 2.