Question

已知x2分之1次方+x-2分之1次方=3求x平方+x-2次方-2分之x2分之3次方+x-2分之3次方-3的值

Answer 1

x^(1/2)+x^(-1/2)=3

求x^2+x^(-2)-(x^(3/2)+x^(-3/2))/2-3

解:

x^(1/2)+x^(-1/2)=3

两边平方,得

x + x^(-1) + 2 = 9

即

x + x^(-1) = 7 . (1)

再平方得

x^2 + x^(-2) + 2 = 49

x^2 + x^(-2) = 47 . (2)

又, (1) (2) 两式相乘得

x^3 + x^(-3) + x + x^(-1) = 7*47

故由(1),

x^3 + x^(-3) = 7*47 - 7 = 7*46=322 ... (3)

于是 (x^(3/2)+x^(-3/2))^2 = x^3+x^(-3)+2=324

x^(3/2)+x^(-3/2)=18或-18.

由于是分数指数, 不允许x