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Question
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 - x2 = 69
⇒ x2 + 9 + 6x - x2 = 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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