已知x2-4x+1=0,求x4+1x4的值.______-数学

题目简介

已知x2-4x+1=0,求x4+1x4的值.______-数学

题目详情

已知x2-4x+1=0,求x4+
1
x4
的值.______
题型:解答题难度:中档来源:不详

答案

∵x2-4x+1=0,
∴x-4+class="stub"1
x
=0,
即x+class="stub"1
x
=4,
∴x2+class="stub"1
x2
=(x+class="stub"1
x
)2-2,
=42-2,
=14,
∴x4+class="stub"1
x4
=(x2+class="stub"1
x2
)2-2,
=142-2,
=194.
故答案为:194.

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