若x^(1/2)-x(-1/2)=3.求[x^(3/2)-x(-3/2)-3]/[x^2+x^(-2)-2]的值
题目
若x^(1/2)-x(-1/2)=3.求[x^(3/2)-x(-3/2)-3]/[x^2+x^(-2)-2]的值
答案
(X^(1/2)-X^(-1/2))^3=27X^(3/2)-3X^(1/2)+3X^(-1/2)-X^(-3/2)=27x^(3/2)-x^(-3/2)-3=33;(X^(1/2)-X^(-1/2))^2=9X-2+X^(-1)=9(X+X^(-1))^2=121X^2+X^(-2)-2=117因此:[X^(3/2)-X(-3/2)-3]/[X^2+X^(-2)-2]=3861...
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