X+Y=-1,XY=3求5(XY+2Y)+(6X-(2XY+Y-3X))的值

问题描述：

答

X+Y=-1, XY=3 级成方程组，
则 X=-1-Y 代入 XY=3
得 (-1-Y)Y=3 -Y-Y^2=3
两边乘以-1，得 Y^2+Y=-3
左边因式分解，得 (Y+0.5)^2=-2.75 无解
你确定不是在忽悠？

答

5(XY+2Y)+(6X-(2XY+Y-3X)
= 5XY+10Y+6X-2XY-Y+3X
=3XY+9Y+9X
带入X+Y=-1,XY=3
5(XY+2Y)+(6X-(2XY+Y-3X)
=3XY+9Y+9X
=3*3+9*（-1）
=0

答

0 Y=-X-1，代入原式，经过合并同类项，得0

答

利用消元法

答

5(XY+2Y)+(6X-(2XY+Y-3X))
=5XY+10Y+(6X-2XY-Y+3X)
=5XY+10Y+6X-2XY-Y+3X
=(5XY-2XY)+(6X+3X)+(10Y-Y)
=3XY+9X+9Y
=3XY+9(X+Y)
=3*3+9*(-1)
=9-9
=0

答

原式=5XY+10Y+6X-2XY-Y+3X=3XY+9Y+9X=3XY+9(X+Y)
把X+Y=-1,XY=3代入原式，得3-9=-6

答

5(XY+2Y)+(6X-(2XY+Y-3X))去掉括号整理得：9（X+Y）+3XY=9×（-1）+3×3=0