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Really really hard var in answer choice

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by sanju09 » Thu Aug 12, 2010 10:11 pm
Jinglander wrote:a b c and d are all posative. ab=c and a/b=d what is a+b


answer is sqrt(cd)*(d+1) /d


This involves some pretty heavy duty algebra. Can you show me

You want answer in terms of c and d only.

If a b = c and a/b = d then a b × a/b = c d or c d = a^2. Now, we can also save b^2 = c^2/a^2 = c^2/ (c d) = c/d for a rainy day.

We can take a + b = b (a/b + 1) or simply a + b = b (d + 1). Now squaring both sides gives

(a + b) ^2 = b^2 (d + 1) ^2

Or (a + b) ^2 = (c/d) (d + 1) ^2

Or (a + b) = √{(c/d) (d + 1) ^2} = (d + 1) √(c/d)


To guarantee a rational denominator, we must multiply √d to the numerator and denominator of the radical. That gives us the final answer as

(a + b) = (d + 1) √(c d)/d
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