Question

已知x^2+x+（1/x^2+x）=2,求2x^2+2x+1的值

Answer 1

令t=x^2+x

x^2+x+（1/x^2+x）=2

t+1/t=2

t^2+1=2t

t^2-2t+1=0

(t-1)^2=0

t=1

x^2+x=1

2x^2+2x+1

=2(x^2+x)+1

=2*1+1

=3