4x^2+4/x^2+12x+12/x=47

X^4-11x^2 + 18 = 0

4 (x² + 1/x²) + 12 (x + 1/x) = 47

x + 1/x = t

x² + 1/x² = (x + 1/x) ² - 2 = t² - 2

4t² - 8 + 12t = 47

4t² + 12t - 55 = 0

D = 144 + 880 = 1024 = 32²

t1 = (-12 - 32) / 8 = - 11/2 = - 5,5

t2 = (-12 + 32) / 8 = 5/2 = 2,5

x + 1/x = - 5,5

x + 5,5x + 1 = 0

D = 30,25 - 4 = 26,25 = (5√1,05) ²

x1,2 = (-5,5 ± 5√1,05) / 2

x + 1/x = 2,5

x² - 2,5x + 1 = 0

D = 6,25 - 4 = 2,25 = (1,5) ²

x3 = (2,5 - 1,5) / 2 = 0,5

x4 = (2,5 + 1,5) / 2 = 2

Ответ: (-5,5 ± 5√1,05) / 2; 0,5; 2

2.

x² = t > 0

t² - 11t + 18 = 0

D = 121 - 72 = 49 = 7²

t1 = (11-7) / 2 = 2

t2 = (11+7) / 2 = 9

x1,2 = ±√2

x3,4 = ±3

Ответ: ±√2; ±3