由x²-3x+1=0同时除以x可得
x-3+1/x=0
可得 x+1/x=3
又有(x+1/x)²=9=x²+1/x²+2
故x²+1/x²=9-2=7
由((x+1/x)²碰判春)²=9²=81=x^4+1/笑耐x^4+2+4(x²+1/冲早x²)+4
可得x^4+1/x^4=81-6-4×7
=47
答:
x²+1=3x,两边除以x得卜尘镇x+1/x=3
两边平方兄亩得:x²+1/x²+2=9,即x²+1/x²=7
再两边平方得:x^4+1/x^4+2=49
所以x^4+1/型粗x^4=47
x+1/x=3
x^4+(1/x)^4=(x+1/x)^2-2=9-2=7
x^2-3x+1=0
利纯察用公式法,解得x=3/2±(√5)/2
x+1/x
=3/2±(√5)/2+1/[3/2±(√慧裤返5)/2]
=3/2±(√5)/2+2/[3/2±(√5)/2]
=3/2±(√5)/2+3/2-+(√5)/2
=3
(x+1/x)^2=9x^2+1/x^2+2=9
x^2+1/x^2=7
(x^2+1/前饥x^2)^2=49
x^4+1/x^4+2=49
x^4+1/x^4=47