Question

(x^2+5x-1)(x^2+5x+5)=55 решите уравнение пожалуйста

Answer 1

x = 1

x = -6

$(x^{2} + 5x - 1) ( x^{2} + 5x +5) = 55\x^{4} +5x^{3} + 5x^{2} + 5x^{3} + 25x - x^{2} - 5x - 5 = 55\\x^{4} + 10x^{3} + 29x^{2}+20x- 5 = 55\\x^{4} + 10x^{3} + 29x^{2} + 20x - 5 - 55 = 0\\x^{4} -x^{3}+11x^{3}-11x^{2}+40x^{2} - 40x + 60x - 60 = 0\\x^{3} (x-1) +11x^{2} (x-1) + 40x(x-1) + 60(x-1) = 0\\(x-1)(x^{3} +11x^{2} + 40x + 60) = 0\\(x-1) (x^{2} (x+6) + 5x(x+6) + 10(x+6)) = 0\\(x-1)(x+6)(x^{2} + 5x + 10) = 0\ \x-1 = 0\x+6 =0\x^{2} + 5x + 10 = 0$