x²-3x+1=0
等式两边同除以x
x-3 +1/x=0
x+ 1/x=3
(1)
x²+1/x²=(x+1/x)²-2=3²-2=7
(2)
x⁴+1/x⁴=(x²+ 1/x²)²-2=7²-2=47
(3)
x²-3x+1=0 x²=3x-1
x⁴+7/x²
=(3x-1)²+ 7/x²
=9x²-6x+1+7/x²
=7(x²+1/x²) +2x²-6x+1
=7(x²+ 1/x²)+2(x²-3x+1)-1
=7×7+0-1
=48
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