杭州交通信息网innisfree小绿瓶功效:初一数学
来源：百度文库 编辑：杭州交通信息网 时间：2024/05/05 19:06:47
已知x=y+z=-2,求x^3+5(y^3+z^3)+15xyz的值
x^3+5(y^3+z^3)+15xyz
=x^3+5(y+z)(y^2-yz+z^2)+15xyz
=x^3+5x(y^2-yz+z^2)+15xyz
=x^3+(5xy^2+5xyz)-5xyz+5xyz+5xz^2+5xyz
=x^3+5xy(y+z)+5xz(z+y)
=x^3+5x^2y+5x^2z
=x^3+5x^3)
=6x^3=6*(-2)^3=-48
x^3+5(y^3+z^3)+15xyz
=(-2)^3+5[(y+z)^3-3(y^2z+yz^2)]+15×(-2)yz
=-8+5[((-2)^3-3yz(y+z)]-30yz
=-8+5(-8+6yz)-30yz
=-8-40+30yz-30yz
=-48