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The difference of two numbers is 3 and the difference of their squares is 69. Find the numbers.

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#### Solution

Let one number = x

Second number = x + 3 [Difference of two numbers is 3]

According to the statement :

(x + 3)^{2} - (x)^{2} = 69

⇒ (x)^{2} + (3)^{2} + 2 × x × 3 - x^{2} = 69

⇒ x^{2} + 9 + 6x - x^{2} = 69

⇒ 6x = 69 - 9

⇒ 6x = 60

⇒ x = `60/6`

⇒ x = 10

One number = 10

Second number = x + 3 = 10 + 3 = 13

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