Question

一道关于完全平方公式数学题已知x^2-3x+1=0,试求①x^2+1/x^2 ②x^4+1/x^4

Answer 1

x^2-3x+1=0,x-3+1/x=0 (因为x不等于0,两边同时除以x)

x+1/x=3

(x+1/x)^2=9

x^2+1/x^2+2=9

x^2+1/x^2=7

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

x^4+1/x^4+2=49

x^4+1/x^4=47

综上x^2+1/x^2=7,x^4+1/x^4=47