Question

若方程x^2+2px-3p-2=0的两个不相等的实数根x1,x2,满足x1^2+x1^3=4-(x2^2+x2^3),则

Answer 1

x1² + x1³ = 4 - (x2² + x2³)

x1² + x2² + x1³ + x2³ = 4

(x1 + x2)² - 2x1x2 + (x1 + x2)[(x1 + x2)² - 3x1x2] = 4

4p² + 2(3p + 2) + (-2p)[4p² + 3(3p+2)] = 4

p(4p + 3)(p + 1) = 0

△ = 4p² + 4(3p + 2) > 0

(p + 1)(p + 2) > 0

p = 0 或 p = -3/4