by 
Anonymous
ANSWERS: 6
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what do I win if I get it right ? 0 & 2
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0 and 0 seem to fit the bill well enough.
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Hmmm.... I'm really stuck on this. I can't see how it can work. In order for the product and quotient to be the same the following must be true- xy = y/x So multiplying by x and dividing by y gives- x^2 = 1 So- x= +-1 (can't do the proper "plus or minus" symbol here!) Substitution gives- (+-)y=(+-)y So y can take any value Now considering the sum and product- y + x = xy So- y +-1 = (+-)y But I can't see how this is true for any value of y. Am I missing something here? The only other values I have seen people use are 0 and 0, but this is not correct as 0/0 is undefined.
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0.5 * -1 = -0.5 0.5 + -1 = -0.5 0.5 / -1 = -0.5
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Jewels Vern I think Quirkie is onto something here.
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Where yy means y squared: xy = x/y xyy = x xyy - x = 0 x(yy - 1) = 0 x(y + 1)(y - 1) = 0 So either x = 0, y = 1 or y = -1. If x = 0: x + y = xy 0 + y = 0y y = 0 but contradiction x/y = 0/0 If y = 1: x + y = xy x + 1 = x no solutions If y = -1: x + y = xy x - 1 = -x 2x - 1 = 0 2x = 1 x = 1/2 solution So the only pair that satisfy the constraints are 1/2 and -1. Verify: 1/2 + (-1) = -1/2 1/2 * (-1) = -1/2 1/2 / (-1) = -1/2 All equal. Q.E.D.
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The number is 0 & 2
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