Question 1107842: x+y+z =0 then find the value of (x+y)(y+z)(x+z)/xyz +11
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! x+y+z =0 then find the value of (x+y)(y+z)(x+z)/xyz +11
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ans: 10
( x,y, and z each nonzero )
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x+y+z=0 —> -x = y+z, -y = x+z, -z = x+y
So
(x+y)(y+z)(x+z)/xyz +11
can be re-written:
(-z)(-x)(-y)/(xyz) + 11 = -1 + 11 = 10, so long as x,y,and z are each nonzero.
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