# Finding the smallest number [closed]

the sum of two positive numbers equals the difference of the squares of the two numbers, which equals the quotient of the larger number when divided by the smaller. What is the smaller number? Provide the exact answer.

## closed as off-topic by Gareth McCaughan♦, Rand al'Thor, Will, Deusovi♦Oct 2 '16 at 23:13

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• "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – Gareth McCaughan, Rand al'Thor, Will, Deusovi
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• It looks like sqrt{2}/2. – Matsmath Oct 2 '16 at 21:09

Let our numbers be $a,b$ where $a<b$. Then we have $a+b=b^2-a^2$, whence either $a+b=0$ (nope, they're positive numbers) or $1=b-a$. And now $a+b=b/a$ means, substituting $b=a+1$, that $2a+1=1+1/a$ or $2a^2=1$ so (since our numbers are positive) $a=1/\sqrt{2}$.