已知x的2次方=x+1,求代数式x的5次方-5x+2的值详细过程

显示全部楼层 · 2012-5-5 20:26:39

x2=x+1以下x2都用x+1代替平方x^4=x2+2x+1=x+1+2x+1=3x+2所以x^5=x(3x+2)=3x2+2x=3(x+1)+2x=5x+3所以原式=5x+3-5x+2=5...

千问 · 2012-5-5 20:26:39

∵x2=x+1
x2-x-1=0
x=(1±√1+4)/2=(1±√5)/2∴x的5次方-5x+2=x2*x2*x-5x+2=(x+1)2*(x+1)2*x-5x+2=(x2+2x+1)(x2+2x+1)*x-5x+2=(x+1+2x+1)(x+1...

千问 · 2012-5-5 20:26:39

x2=x+1x5-5x+2=x(x4-1)+2=x(x2+1)(x2-1)+2=x(x+2)x+2=x2(x+2)+2=(x+1)(x+2)+2=x2+3x+4=4x2+1=(-1±√3i)2+1=2√3i-1 ……貌似算错了……...

千问 · 2012-5-5 20:26:39

x^2=x+1,x^5-5x+2=x^5-x-4x+2=x(x^4-1)-4x+2=x(x^2+1)(x^2-1)-4x+2=x(x+2)x-4x+2=x^2(x+2)-4x+2=(x+1)(x+2)-4x+2=x^2+3x+2-4x+2=x+1-x+4=5...

千问 · 2012-5-5 20:26:39

x2=x+1;x=1+1/x; x-1/x=1x2-x-1=0(x-1/x)2=x2+1/x2-2=1x2+1/x2=3x^5-5x+2=x^3(x2+1/x2)-6x+2=3x^3-6x+2=3x2(x-1/x)-3x+2=3x2-...

已知x的2次方=x+1,求代数式x的5次方-5x+2的值 详细过程