Решите биквадратное уравнение: 1) x^4-29x^2+100=02) 4y^4-5y^2+1=03) 7z^4-19x^2-36=04) y^4-8y^2+4=0

1)

x^4 - 29x^2 + 100 = 0; D = 29^2 - 4 * 100 = 841 - 400 = 441 = 21^2; x^2 = (29 ± 21) / 2;

a) x^2 = (29 - 21) / 2 = 8/2 = 4;

x = ±2;

b) x^2 = (29 + 21) / 2 = 50/2 = 25;

x = ±5.

2)

4y^4 - 5y^2 + 1 = 0; D = 5^2 - 4 * 4 = 25 - 16 = 9 = 3^2; y^2 = (5 ± 3) / 8;

a) y^2 = (5 - 3) / 8 = 2/8 = 1/4;

y = ±1/2;

b) y^2 = (5 + 3) / 8 = 8/8 = 1;

y = ±1.

3)

7z^4 - 19z^2 - 36 = 0; D = 19^2 + 4 * 7 * 36 = 361 + 1008 = 1369 = 37^2; z^2 = (19 ± 37) / 14;

a) z^2 = (19 - 37) / 14 = - 18/14 = - 9/7 < 0 - нет решений;

b) z^2 = (19 + 37) / 14 = 56/14 = 4;

z = ±2.

4)

y^4 - 8y^2 + 4 = 0; D/4 = 4^2 - 4 = 12; y^2 = 4 ± √12; y = ±√ (4 ± √12).

Ответ:

1) ±2; ±5; 2) ±1/2; ±1; 3) ±2; 4) ±√ (4 ± √12).