Question

急!高一数学必修一人教A版第60页习题2.1B组第二题

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.