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