Question

已知x²+x-6=0 求3x4次+6x³+3x²

Answer 1

x²+x-6=0
x²+x=6
3x^4+6x³+3x²
=3x²(x²+x)-3x³+6x³+3x²
=18x²+3x³+3x²
=21x²+3x³
=21x²+3(x-1)(x²+x+1)+3
=21x²+21(x-1)+3
=21(x²+x)-21+3
=126-18
=108

Answer 2

因为

x²+x=6

3x4+6x3+3x²
=3x²(x²+2x+1)
=3x²(x²+x+x+1)
=3x²(6+x+1)
=3x²(x+7)
=3x3+21x²
=3x(x²+7x)
=3x(x²+x+6x)
=3x(6x+6)
=18x²+18x
=18(x²+x)
=18x6
=108