已知x²-4x+4与|y—1|互为相反数,则式子(1/x+1/y)÷(x²+2xy+y²)/xy的值等于?
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![已知x²-4x+4与|y—1|互为相反数,则式子(1/x+1/y)÷(x²+2xy+y²)/xy的值等于?](/uploads/image/z/2602001-65-1.jpg?t=%E5%B7%B2%E7%9F%A5x%26%23178%3B-4x%2B4%E4%B8%8E%7Cy%E2%80%941%7C%E4%BA%92%E4%B8%BA%E7%9B%B8%E5%8F%8D%E6%95%B0%2C%E5%88%99%E5%BC%8F%E5%AD%90%EF%BC%881%2Fx%2B1%2Fy%EF%BC%89%C3%B7%EF%BC%88x%26%23178%3B%2B2xy%2By%26%23178%3B%EF%BC%89%2Fxy%E7%9A%84%E5%80%BC%E7%AD%89%E4%BA%8E%3F)
已知x²-4x+4与|y—1|互为相反数,则式子(1/x+1/y)÷(x²+2xy+y²)/xy的值等于?
已知x²-4x+4与|y—1|互为相反数,则式子(1/x+1/y)÷(x²+2xy+y²)/xy的值等于?
已知x²-4x+4与|y—1|互为相反数,则式子(1/x+1/y)÷(x²+2xy+y²)/xy的值等于?
即(x-2)²+|y-1|=0
所以x-2=0,y-1=0
x=2,y=1
所以原式=(x+y)/xy÷(x+y)²/xy
=1/(x+y)
=1/3
因为x²-4x+4与|y—1|为非负数
所以x²-4x+4=|y—1|=0
所以x=2 y=1
所以(1/x+1/y)÷(x²+2xy+y²)/xy=1/18
x²-4x+4=-|y—1|
(x-2)^2+|y—1|=0
所以x=2 y=1
(1/x+1/y)÷(x²+2xy+y²)/xy
=(3/2)÷(x+y)^2/xy
=(3/2)÷9/2
=1/3
因为x²-4x+4=(x-2)²≥0,|y—1|≥0,且它们互为相反数
所以:x²-4x+4=0, |y—1|=0
所以:x=2,y=1
所以:(1/x+1/y)÷(x²+2xy+y²)/xy=[(1/2)+1]/(4+4+1)/2=1/12