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Question
The difference between two numbers is 14 and the difference between their squares is 448. Find the numbers.
Solution
Let the larger number be x and the smaller number be y.
Then, we have:
x – y = 14 or x = 14 + y ……….(i)
`x^2 – y^2 = 448` ………(ii)
On substituting x = 14 + y in (ii) we get
`(14 + y)^2 – y^2 = 448`
`⇒ 196 + y^2 + 28y – y^2 = 448`
⇒ 196 + 28y = 448
⇒ 28y = (448 – 196) = 252
`⇒ y = 252/28 = 9`
On substituting y = 9 in (i), we get:
x = 14 + 9 = 23
Hence, the required numbers are 23 and 9.
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