急.数学指数运算..设x>0,若x^(1/2) + x^(-1/2) =3,求[x^2+(x^-2) -2] / [x^
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急.数学指数运算.
.设x>0,若x^(1/2) + x^(-1/2) =3,求[x^2+(x^-2) -2] / [x^(3/2) +x^(-3/2)-3]
.设x>0,若x^(1/2) + x^(-1/2) =3,求[x^2+(x^-2) -2] / [x^(3/2) +x^(-3/2)-3]
![急.数学指数运算..设x>0,若x^(1/2) + x^(-1/2) =3,求[x^2+(x^-2) -2] / [x^](/uploads/image/z/17359581-21-1.jpg?t=%E6%80%A5.%E6%95%B0%E5%AD%A6%E6%8C%87%E6%95%B0%E8%BF%90%E7%AE%97..%E8%AE%BEx%3E0%2C%E8%8B%A5x%5E%281%2F2%29+%2B+x%5E%28-1%2F2%29+%3D3%2C%E6%B1%82%5Bx%5E2%2B%28x%5E-2%29+-2%5D+%2F+%5Bx%5E)
[x^(1/2) + x^(-1/2)]^2 =(x+x^-1)+2=9 x+x^-1=7 x+x^=8
[x^(1/2) + x^(-1/2)]^3=x^(3/2) +x^(-3/2)+3[x^(1/2) + x^(-1/2)]=x^(3/2) +x^(-3/2)+9
原式=(x+x^-1)^2-4/[x^(1/2) + x^(-1/2)]^3-12=60/15=4
[x^(1/2) + x^(-1/2)]^3=x^(3/2) +x^(-3/2)+3[x^(1/2) + x^(-1/2)]=x^(3/2) +x^(-3/2)+9
原式=(x+x^-1)^2-4/[x^(1/2) + x^(-1/2)]^3-12=60/15=4
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