1.x^(-1/2) + x^1/2 =3,求① x^(-2/3) + x^2/3 的值 ② x^(-3) + x^3
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1.x^(-1/2) + x^1/2 =3,求① x^(-2/3) + x^2/3 的值 ② x^(-3) + x^3 的值
2.若5^m =4,5^n =3 ,求5^ 2m-4n/3的值 (注:2m-4n 为一整体除以3.2m-4n/3都是指数)
2.若5^m =4,5^n =3 ,求5^ 2m-4n/3的值 (注:2m-4n 为一整体除以3.2m-4n/3都是指数)
(1)①x+x^(-1)= [x^(-1/2) + x^1/2]²-2=7
∴x^(-2/3) + x^2/3=[x+x^(-1)]*[x^(-1/2) + x^1/2]- [x^(-1/2) + x^1/2]
=7*3-3
=18
② x^(-3) + x^3=x^[(-2/3) + x^2/3]²-2=322
(2)5^ (2m-4n)/3
=5^(2m/3)÷5^(4n/3)
=(5^m)^(2/3)÷(5^n)^(4/3)
=4^(2/3)÷3^(4/3)
=(2/3)^(4/3)
∴x^(-2/3) + x^2/3=[x+x^(-1)]*[x^(-1/2) + x^1/2]- [x^(-1/2) + x^1/2]
=7*3-3
=18
② x^(-3) + x^3=x^[(-2/3) + x^2/3]²-2=322
(2)5^ (2m-4n)/3
=5^(2m/3)÷5^(4n/3)
=(5^m)^(2/3)÷(5^n)^(4/3)
=4^(2/3)÷3^(4/3)
=(2/3)^(4/3)
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