Question

已知X2+2X=3,求代数式X4+7X3+8X2-13X+15的值

已知X2+2X=3,求代数式X4+7X3+8X2-13X+15的值
注：X4为X的4次方，X为字母

Answer 1

由x2+2x=3知，x2=3-2x，代入得，原式=(3-2x)2+7x(3-2x)+8(3-2x)-13x+15=-10x2-20x+48=-10(3-2x)-20x+48=18

Answer 2

X^2+2X=3
x^2+2x-3=0

X^4+7X^3+8X^2-13X+15
=x^4+2x^3-3x^2+5x^3+11x^2-13x+15
=x^2(x^2+2x-3)+5(x^3+2x^2-3x)+x^2+15x-13x+15
=x^2+2x+15
=18