solution of (ab)/(a+b)=2 Watch

tanno1992
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Does the equation (ab)/(a+b)=2 have an infinite number of solutions?
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Unbounded
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Depends; if a and b are integers, no; if a and b are reals, yes.
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tanno1992
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thanks, what if just one is an integer? also, how can you prove it?
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nuodai
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(Original post by sallon)
thanks, what if just one is an integer? also, how can you prove it?
Say a is some fixed integer. You can rearrange the equation to get b in terms of a; then for any possible value of a (i.e. integers which don't make you end up dividing by zero) there will be a value of b which satisfies the equation -- it must satisfy it, since all you did was rearrange. So if there is an infinite number of possible values for a, then there is an infinite number of values of b, so there are an infinite number of solutions to the equation.
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