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The sum of two numbers is 29 and the difference of their square is 145 . Find their difference.

Solution :

Let the number be $a$ and $b$.

$\therefore$ According to question,

$a+b=29$...(1)

and $a^{2}-b^{2}=145 \quad$...(2)

We know that,

\begin{aligned} & a^{2}-b^{2}=(a+b)(a-b) \\ \Rightarrow & 145=29(a-b) \\ \therefore \quad & a-b=\frac{145}{29}=5 ; \text { Ans. } \end{aligned}

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