Question

谁会?一.已知X^2+X-1=0,求X^3-2X+4的值二.已知a^2-3a+1=0,求a^4+1/a^4的值

Answer 1

X^3-2X+4

=X（X^2+X-1）-（X^2+X-1）+3

=3

a^4+1/a^4

=a^4+1/a^4+2-2

=(a^2+1/a^2)^2-2

因为a^2-3a+1=0 a不等于0

a^2+1=3a 两边同除以a

所以a+1/a=3

所以(a^2+1/a^2)^2-2

=[（a+1/a）^2-2]^2-2

=(3*3-2)^2-2

=47