Question

已知x^2+1=2x两边同除以x后,得x+1/x=2,则(x+1/x)^2=2^2,用完全平方公式,可得x^2+2+(1

Answer 1

1

一定x≠0,否则代入原方程得到1=0;

则x^2+1=5x;

→x+1/x=5.

(x+1/x)^2 =25,按完全平方公式展开得

→x^2+1/x^2=23

2

x^2+1/x^2=47→(x+1/x)^2 =x^2 +2+ 1/x^2 = 49

→x+1/x =±7

x^2 +1 =±7x

x^2±7x =-1