4 х⁴-17 х²+4=0 4 х⁴-37²+9=0 х⁴-7 х2+12=0

4 х^4 - 17 х^2 + 4 = 0

Сделаем замену. Пусть t = x^2

4 х^4 - 17 х^2 + 4 = 0.

4t^2 - 17t + 4 = 0.

D = b^2 - 4ac.

t1 = ( - b + √ D) / 2a.

t2 = ( - b - √ D) / 2a.

D = (-17) ^2 - 4 * 4 * 4.

D = 289 - 64 = 225.

t1 = (17 + 15) / 2 * 8 = 2.

t2 = (17 - 15) / 2 * 8 = 1/8.

t = x^2.

t1 = 2.

x1 = √ 2.

t2 = 1/8.

x2 = √ 1/8.

4 х⁴ - 37² + 9 = 0.

4x^4 = 1369 - 9.

4x^4 = 1360.

x^4 = 1360 / 4.

x^4 = 340.

x = √ √ 340.

x = √ (2√85).

х^4 - 7 х^2 + 12 = 0.

Сделаем замену. Пусть t = x^2.

t^2 - 7t + 12 = 0.

D = b^2 - 4ac.

t1 = ( - b + √ D) / 2a.

t2 = ( - b - √ D) / 2a.

D = (-7) ^2 - 4 * 1 * 12.

D = 49 - 48 = 1.

t1 = (7 + 1) / 2 * 1 = 4.

t2 = (7 - 1) / 2 * 1 = 3.

t = x^2.

t1 = 4.

x1 = 2, - 2.

t2 = 3.

x2 = √ 3