(2x+y)2-(2x-y)(x+y)-2(x-2y)(x+2y),其中x= ,y=-2 化简求值
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(2x+y)2-(2x-y)(x+y)-2(x-2y)(x+2y),其中x= ,y=-2 化简求值
x+y+z=4,x²+y²+z²=2,求xy+yz+zx的值
x+y+z=4,x²+y²+z²=2,求xy+yz+zx的值
(2X+Y)^2-(2X-Y)(X+Y)-2(X-2Y)(X+2Y)
解原式=4X^2+Y^2+4XY-2X^2-2XY+XY+Y^2-2(X^2-4Y^2)
=4X^2+Y^2+4XY-2X^2-2XY+XY+Y^2-2X^2+8Y^2
=4X^2-2X^2-2X^2+Y^2+Y^2+8Y^2+4XY-2XY+XY
=10Y^2+3XY
把x= ,y=-2代入就行了.
x+y+z=4,x²+y²+z²=2,求xy+yz+zx的值
(x+y+z)^2=x^2+y^2+z^2+2(xy+xz+yz)
16=2+2(xy+xz+yz)
故zx+xy+yz=7
解原式=4X^2+Y^2+4XY-2X^2-2XY+XY+Y^2-2(X^2-4Y^2)
=4X^2+Y^2+4XY-2X^2-2XY+XY+Y^2-2X^2+8Y^2
=4X^2-2X^2-2X^2+Y^2+Y^2+8Y^2+4XY-2XY+XY
=10Y^2+3XY
把x= ,y=-2代入就行了.
x+y+z=4,x²+y²+z²=2,求xy+yz+zx的值
(x+y+z)^2=x^2+y^2+z^2+2(xy+xz+yz)
16=2+2(xy+xz+yz)
故zx+xy+yz=7
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