Question

急急急！高一数学必修一人教A版第60页习题2.1B组第二题

急急急！高一数学必修一人教A版第60页习题2.1B组第二题
已知x+（x^-1）=3，求下列各数的值：
(x^1/2)+(x^-1/2)=？ (x^2)+(x^-2)=？ (x^2)-(x^-2)=?
答案我知道，但是我不会做，求各位帮帮忙……

Answer 1

1.因为[(x^1/2)+(x^-1/2)]^2
=x+(x^-1)+2
=3+2
=5,
且(x^1/2)+(x^-1/2)>0,
所以(x^1/2)+(x^-1/2)=根号5；

2.因为[x+(x^-1)]^2
=(x^2)+(x^-2)+2
=3^2=9,
所以(x^2)+(x^-2)=7；

3.因为[x-(x^-1)]^2
=(x^2)+(x^-2)-2
=7-2=5,
所以x-(x^-1)=根号5或-根号5，
所以(x^2)-(x^-2)
=[x+(x^-1)][x-(x^-1)],
因为x+(x^-1)=3,x-(x^-1)=根号5或-根号5，
所以(x^2)+(x^-2)=3根号5或-3根号5.

Answer 2

[(x^1/2)+(x^-1/2)]^2=x+（x^-1)+2=3+2=5
所以（x^1/2)+(x^-1/2)=根号5
(x^2)+(x^-2)=[x+（x^-1）]^2-2=7
(x^2)-(x^-2)=（ x+x^-1)(x-x^-1)=3(x-x^-1)