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若x^(1/2)-x(-1/2)=3.求[x^(3/2)-x(-3/2)-3]/[x^2+x^(-2)-2]的值
题目详情
若x^(1/2)-x(-1/2)=3.求[x^(3/2)-x(-3/2)-3]/[x^2+x^(-2)-2]的值
▼优质解答
答案和解析
（X^(1/2)-X^(-1/2))^3=27
X^(3/2)-3X^(1/2)+3X^(-1/2)-X^(-3/2)=27
x^(3/2)-x^(-3/2)-3=33;
（X^(1/2)-X^(-1/2))^2=9
X-2+X^(-1)=9
(X+X^(-1))^2=121
X^2+X^(-2)-2=117
因此：[X^(3/2)-X(-3/2)-3]/[X^2+X^(-2)-2]=3861
X^(3/2)-3X^(1/2)+3X^(-1/2)-X^(-3/2)=27
x^(3/2)-x^(-3/2)-3=33;
（X^(1/2)-X^(-1/2))^2=9
X-2+X^(-1)=9
(X+X^(-1))^2=121
X^2+X^(-2)-2=117
因此：[X^(3/2)-X(-3/2)-3]/[X^2+X^(-2)-2]=3861
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