4x^2+4/x^2+12x+12/x=47 x^4-11x^2+ 18= 0 - вопрос №696284142421212474112180 от Imdoingfinetoday123 31.12.2022 10:00

Question

Математика: 4x^2+4/x^2+12x+12/x=47 x^4-11x^2+ 18= 0

Imdoingfinetoday123 · Answer

4(x² + 1/x²) + 12(x + 1/x) = 47x +1/x = tx² + 1/x² = (x + 1/x)² - 2 = t² - 24t² - 8 + 12t =474t² +12t - 55 = 0D = 144 + 880 = 1024 = 32²t1 = (-12 - 32)/8 = -11/2 = -5,5t2 = (-12 + 32)/8 = 5/2 = 2,5x + 1/x = -5,5x + 5,5x + 1 = 0D = 30,25 - 4 = 26,25 = (5√1,05)²x1,2= (-5,5 ± 5√1,05)/2x + 1/x = 2,5x² - 2,5x + 1 = 0D = 6,25 - 4 = 2,25 = (1,5)²x3 = (2,5 - 1,5)/2 = 0,5x4 = (2,5 + 1,5)/2 = 2ответ: (-5,5 ± 5√1,05)/2; 0,5; 22.x² = t 0t² - 11t + 18 = 0D = 121 - 72 = 49 = 7²t1 = (11-7)/2 = 2t2 = (11+7)/2 =...