Question

已知x^2+x=1/3,求6x^4+15x^3+10x^2

Answer 1

(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