Question

已知a²-a-1=0，求代数式a四次方-3a+2的值

Answer 1

因为a²-a-1=0，所以a²=a+1,a²-a=1
a四次方-3a+2=（a²）²-3a+2
=(a+1)²-3a+2
=a²+2a+1-3a+2
=a²-a+3
=1+3
=4
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Answer 2

您好：

a²-a-1=0
a²-a=1

a四次方-3a+2
=a的4次方-a³+a³-3a+2
=a²（a²-a）+a³-3a+2
=a²+a³-3a+2
=a³-a²+2a²-3a+2
=a(a²-a)+2a²-3a+2
=a+2a²-3a+2
=2（a²-a）+2
=2+2
=4

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Answer 3

A方-A-1=0
A方-1=A
A方-A=1

A四-3A+2
=(A方-1)方+1+2A方-3A
=A方+1+2A方-3A
=3(A方-A)+1
=3+1
=4

Answer 4

a²-a=1
a四次方-3a+2
=a^4-a^3+a^3-a^2+a^2-a-2a+2
=a^2+a+1-2a+2
=a^2-a+3
=4

Answer 5

a^4-3a+2
=(a+1)^2 -3a+2
= a^2-a+3
= 4