Решите математику t в четвёртой степени - 17t во второй+16=0 xчетвёртой степени - 29x во второй+100=0 Xчетвёртой степени+32x во второй-144=0 Vчетвёртой степени+26 v во второй+25=0

1) t^4 - 17t^2 + 16 = 0.

Введем замену t^2 = x.

x^2 - 17t + 16 = 0;

D = b^2 - 4ac = 289 - 4 * 16 = 225.

x1 = (-b + √D) / 2a = (17 + 15) / 2 = 16.

x2 = (-b - √D) / 2a = (17 - 15) / 2 = 1.

Вернёмся к замене:

t^2 = 16;

t12 = ±4;

t^2 = 1;

t34 = ±1.

2) x^4 - 29x^2 + 100 = 0.

Замена х^2 = t.

t^2 - 29t + 100 = 0.

D = 841 - 400 = 441.

t1 = (29 + 21) / 2 = 25.

t2 = (29 - 21) / 2 = 4.

x^2 = 25;

x12 = ±5.

x^2 = 4.

x34 = ±2.

3) x^4 + 32x^2 - 144 = 0.

Замена х^2 = t:

t^2 + 32t - 144 = 0;

D = 1024 + 576 = 1600.

t1 = (-32 + 40) / 2 = 4.

t2 = (-32 - 40) / 2 = - 36.

x^2 = 4;

x12 = ±2.

x^2 = - 36;

x34 = ±6i.

4) v^4 + 26v^2 + 25 = 0.

Замена v^2 = x.

x^2 + 26x + 25 = 0.

D = 676 - 100 = 576.

x1 = (-26 + 24) / 2 = - 1;

x2 = (-26 - 24) / 2 = - 25.

v^2 = - 1;

v = 1i;

v^2 = - 25;

v = 5i.