Question

已知函数x+x^-1=3则x^（3／2）+x^（-3／2）的值为

Answer 1

令 a = x^(1/2) ,b = x^(-1/2) ,则：ab = 1已知,x^+x^（-1）=3,即a^2+b^2 = 3(a+b)^2=a^2+b^2+2ab=3+2=5a +b=±√5x^（3／2）+x^（-3／2）=a^3+b^3=(a+b)(a^2+b^2-ab)=±√5*（3-1）=±2√5