Question

化简求值,若x的平方减x再减1等于0,求x的五次方减5x的值

Answer 1

x²-x-1=0

x²=x+1

x²-x=1

所以

x^5-5x

=x³(x+1)-5x

=x^4+x³-5x

=（x+1）²+x(x+1)-5x

=x²+2x+1+x²+x-5x

=2x²-2x+1

=2(x²-x)+1

=2×1+1

=3