Question

x^2+(x/(x+1))^2=3,求所有实数根的和？

注意：实数根

Answer 1

方程化简为
x^4 + 2x^3 - x^2 - 6x - 3 = 0
x^4 - x^3 - x^2 + 3x^3 - 3x^2 - 3x - + 3x^2 - 3x - 3 = 0
x^2(x^2-x-1) + 3x(x^2-x-1) + 3(x^2-x-1) = 0
(x^2+3x+3)(x^2-x-1) = 0
方程x^2+3x+3=0无实数根
所以实数根的和是1