Question

化简求值(2x+y)(x-2y)-2x(x+y),其中x,y满足x的平方加y的平方减2x加4y等于-5

Answer 1

x²+y²-2x+4y=-5
x²+y²-2x+4y+5=0
(x-1)²+(y+2)²=0
由非负性
x-1=0
y+2=0
解得
x=1
y=-2

(2x+y)(x-2y)-2x(x+y)
=2x²-3xy-2y²-2x²-2xy
=-5xy-2y²
=-5×1×(-2)-2×(-2)×(-2)
=10-8
=2

Answer 2

x的平方加y的平方减2x加4y等于-5
(x-1)^2+(y+2)^2=0
x=1 y=-2
(2x+y)(x-2y)-2x(x+y)
=2x^2+xy-4xy-2y^2-2x^2-2xy
=-5xy-2y^2
=10-8=2
祝你好运

Answer 3

2x^2+xy-4xy-2y^2-2x^2-2xy=-5xy-2y^2
x^2+y^2-2x+4y=-5 (x-1)^2+(y+2)^2=0
x=1,y=-2
当x=1,y=-2
-5xy-2y^2=-5×1×（-2）-2×（-2）^2=10-8=2

Answer 4

x的平方加y的平方减2x加4y等于-5可以化为：(x-1)^2+(y+2)^2=0,所以x=1,y=-2,代入(2x+y)(x-2y)-2x(x+y),得2

Answer 5

你把-5移到右边可以得到x减1的平方加上y加2的平方等于零，所以x=1，y=-2。求得结果为2