Question

【高一数学】一道计算题目》》》》》》

Answer 1

(1)

令x^(1/2)=t 则x^(-1/2)=1/t

t+1/t=3

(1)

x+x^(-1)

=t^2+1/t^2

=(t+1/t)^2-1

=9-1

=8

(2)

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

=t^3+1/t^3+2

=(t+1/t)(t^2-1+1/t^2)+2

=3[(t+1/t)^2-3]+2

=3*(9-3)+2

=20

x^2+x^(-2)+3

=t^4+1/t^4+3

=(t^2+1/t^2)^2+1

=64+1

=65

则[x^(3/2)+x^(-3/2)+2]/[x^2+x^-2+3]

=20/65

=4/13