作业帮高一数学[指数概念的扩充]一道题已知x^(1/2)+x^(-1/2)=3,求[x^2+x^(-2)-2]/[x^(3/2)+x(-3/2)-3]的值
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![高一数学[指数概念的扩充]一道题已知x^(1/2)+x^(-1/2)=3,求[x^2+x^(-2)-2]/[x^(3/2)+x(-3/2)-3]的值](/uploads/image/z/7177402-10-2.jpg?t=%E9%AB%98%E4%B8%80%E6%95%B0%E5%AD%A6%5B%E6%8C%87%E6%95%B0%E6%A6%82%E5%BF%B5%E7%9A%84%E6%89%A9%E5%85%85%5D%E4%B8%80%E9%81%93%E9%A2%98%E5%B7%B2%E7%9F%A5x%5E%281%2F2%29%2Bx%5E%28-1%2F2%29%3D3%2C%E6%B1%82%5Bx%5E2%2Bx%5E%28-2%29-2%5D%2F%5Bx%5E%283%2F2%29%2Bx%28-3%2F2%29-3%5D%E7%9A%84%E5%80%BC)
高一数学[指数概念的扩充]一道题已知x^(1/2)+x^(-1/2)=3,求[x^2+x^(-2)-2]/[x^(3/2)+x(-3/2)-3]的值
高一数学[指数概念的扩充]一道题
已知x^(1/2)+x^(-1/2)=3,求[x^2+x^(-2)-2]/[x^(3/2)+x(-3/2)-3]的值
高一数学[指数概念的扩充]一道题已知x^(1/2)+x^(-1/2)=3,求[x^2+x^(-2)-2]/[x^(3/2)+x(-3/2)-3]的值
x^(1/2)+x^(-1/2)=3※
※式两边平方,得
x+x^-1=7.
再平方得
x^2+x^(-2)=47
※式两边立方,得
x^(3/2)+x(-3/2)+3[x^(1/2)+x^(-1/2)]
=x^(3/2)+x(-3/2)+9
=27
故x^(3/2)+x(-3/2)=18
[x^2+x^(-2)-2]/[x^(3/2)+x(-3/2)-3]
=(47-2)/(18-3)
=3.
x^(1/2)+x^(-1/2)=3
x+1/x=[x^(1/2)+x^(-1/2)]^2-2=7
x^2+x^(-2)=(x+1/x)^2-2=47
x^(3/2)+x^(-3/2)=[x^(1/2)+x^(-1/2)][x-1+1/x]
=3*(7-1)=18
原式=(47-2)*(18-3)=45*15=675
x^(1/2)+x^(-1/2)=3,所以平方得x+2+1/x=9,x+1/x=7,所以x^2+2+x^(-2)=49
所以x^2+x^(-2)=47,x^2+x^(-2)-2=45
[x^(3/2)+x(-3/2)]^2
=x^3+2+x^(-3)=(x+1/x)[x^2-1+x^(-2)]+2=3*46+2=130
所以x^(3/2)+x(-3/2)=根号130(负的舍去)
所以可以求出来了