X^2+2X=3 求x^4+7x^3+8x^2-13+15

来源：学生作业学帮网编辑：学帮网时间：2024/05/13 05:51:17

x^4+7x^3+8x^2-13+15
是不是漏了个x?
x^4+7x^3+8x^2-13x+15
=x^4+2x^3+5x^3+8x^2-13x+15
=x^2(x^2+2x)+5x^3+8x^2-13x+15
=3x^2+5x^3+8x^2-13x+15
=5x^3+10x^2+x^2-13x+15
=5x(x^2+2x)+x^2-13x+15
=15x+x^2-13x+5
=x^2+2x+5
=3+5
=8

X^2+2X=3 =>x=1或x=-3
当x=1时，x^4+7x^3+8x^2-13+15=18
当x=-3时，x^4+7x^3+8x^2-13+15=-34

-24 或者28

X^2+2X=3
即（X+1)^2=4,得X=1或X=-3
当X=1时，x^4+7x^3+8x^2-13+15＝18
当X=-3时，x^4+7x^3+8x^2-13+15＝－21

解方程得:(x-1)(x+3)=0
x=1,或x=-3
代入得,1^4+7*1^3+8*1^2+2=18
或(-3)^4+7*(-3)^3+8*(-3)^2+2=-15

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