x^4-4x^2+1=0,则x^4+x^(-4)=

显示全部楼层 · 2009-2-21 14:30:57

x^4-4x^2+1=0,则x^4+x^(-4)=？
过程

千问 · 2009-2-21 14:30:57

x^4-4x^2+1=0,x≠0,两边同除以x^2得:x^2-4+1/x^2=0x^2+1/x^2=4两边平方得x^4+2+1/x^4=16x^4+x^(-4)=16-2=14...

千问 · 2009-2-21 14:30:57

x^4-4x^2+1=0x^4+1=4x^2x^2+1/x^2=4x^4+1/x^4+2=4x^4+1/x^4=2x^4+x^(-4)=2...

千问 · 2009-2-21 14:30:57

x^4-4x^2+1=0 两边除以x^4得x^(-4)-4x^(-2)+1=0将x^2项移到等式右边x^4+1=4x^2x^(-4)+1=4x^(-2)两等式相乘得1+x^4+x^(-4)+1=16x^4+x^(-4)=14...