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

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Solution —

Let the number be a and

∴ According to the question,

   a + b = 29      ..........(1)

and a2 - b=145    ..........(2)

We know that,

also  a2 - b= ( a + b ) ( a - b)

⇒ 145 = 29 (a - b)

∴ a - b = 145 / 29 = 5

Hence, Their difference is 5

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