Question

【(x+2y)的平方-(x-2y)的平方-(x+2y)(x-2y)-4y】÷2x 已知x的平方+y的平方-4X+y+4分之17=0 化简求值

Answer 1

【(x+2y)的平方-(x-2y)的平方-(x+2y)(x-2y)-4y】÷2x
=(x²+4xy+4y²-x²+4xy-4y²-x²+4y²-4y)÷2x
=(-x²+8xy+4y²-4y)÷2x
x的平方+y的平方-4X+y+4分之17=0
x²-4x+4+y²+y+1/4-4-1/4+17/4=0
(x-2)²+(y+1//2)²=0
(x-2)²=0 (y+1/2)=0
x=2 y=-1/2
把x=2 y=-1/2代人化简式得：
[-2²+8×2×(-1/2)+4×(-1/2)-4×(-1/2)]÷(2×2)
=(-4+8-2+2)÷4
=4÷4
=1

Answer 2

x^2+y^2-4x+y+17/4=0
=>(x-2)^2+(y+1/2)^2=0
=>x=2, y=-1/2
代入上式求值就可以啦。
[(x+2y)^2-(x-2y)^2-(x+2y)(x-2y)-4y]/2x
=(8xy-x^2+4y^2-4y)/2x=-9/4