已知x+y=-4,xy=-12,求y+1x+1+x+1y+1
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已知x+y=-4,xy=-12,求
+
y+1 |
x+1 |
x+1 |
y+1 |
![已知x+y=-4,xy=-12,求y+1x+1+x+1y+1](/uploads/image/z/15129858-66-8.jpg?t=%E5%B7%B2%E7%9F%A5x%2By%3D-4%EF%BC%8Cxy%3D-12%EF%BC%8C%E6%B1%82y%2B1x%2B1%2Bx%2B1y%2B1)
原式=
(y+1)2+(x+1)2
(x+1)(y+1)
=
x2+y2+2(x+y)+2
xy+x+y+1
=
(x+y)2−2xy+2(x+y)+2
xy+x+y+1
∵x+y=-4,xy=-12,
∴原式=
16+24−8+2
−12−4+1=−
34
15.
(y+1)2+(x+1)2
(x+1)(y+1)
=
x2+y2+2(x+y)+2
xy+x+y+1
=
(x+y)2−2xy+2(x+y)+2
xy+x+y+1
∵x+y=-4,xy=-12,
∴原式=
16+24−8+2
−12−4+1=−
34
15.
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