分数指数x+x^(-1)=4x^(1/2)+x^(-1/2)=?x^(3/2)+x^(-3/2)=?x^(1/2)-x^(-1/2)=?解题详细点.

Question

分数指数 x+x^(-1) =4
x^(1/2)+x^(-1/2)=?
x^(3/2)+x^(-3/2)=?
x^(1/2)-x^(-1/2)=?
解题详细点.

Answer 1

∵x+(1/x)=4.∴x＞0.===>(1).[(√x)+(1/√x)]²=6.===>(√x)+(1/√x)=√6.(3)[(√x)-(1/√x)]²=2.===>(√x)-(1/√x)=±√2.(2)原式=[(√x)+(1/√x)]×[x+(1/x)-1]=(√6)×(4-1)=3√6.