已知x^2+x=1/3,求6x^4+15x^3+10x^2

已知x^2+x=1/3,求6x^4+15x^3+10x^2
已知x^2+x=1/3,求6x^4+15x^3+10x^2

已知x^2+x=1/3,求6x^4+15x^3+10x^2
(1)x^2+x=1/3
6x^4+15x^3+10x^2
=6x^2(x^2+x)+9x(x^2+x)+x^2
=2x^2+3x+x^2
=3(x^2+x)
=1
(2)x^2+x=1/3
3x^2+3x-1=0
6x^4+15x^3+10x^2=(3x^2+3x-1)(2x^2+3x+1)+1=1