The difference of two numbers is 3 and difference of their square is 69 find the numbers

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Solution

Let the numbers be a, b.
a - b = 3 ------(i)
a² - b²= 69 and a²- b² = (a + b)(a - b)
⇒ (a + b)(a - b) = 69
⇒ (a + b)(3) = 69
⇒ (a + b) = 69/3 = 23 (ii)
adding equation (i) and (ii) we get
2a = 26
⇒ a = 26/2 = 13
⇒ b = 13 - 3 = 10

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