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Question
Two natural numbers differ by 4. If the sum of their square is 656, find the numbers.
Solution
Let the two numbers be x and y. Then, as per the question,
x2 + y2 = 656 ...... (i)
and x - y = 4
⇒ x = 4 + y ........ (ii)
Putitng 2nd equation in first, we get:
(y+4 )2 + y2 = 656,
⇒ 2y2 + 8y - 640 = 0
⇒ y2 + 4y - 320 = 0
⇒ y2 + 20y -16y- 320 = 0
⇒ y(y+ 20) - 16 (y+20) = 0
⇒ (y-16 ) (y+ 20) = 0
y can't be negative, hence y= 16
x= y+4 = 20
Hence numbers are 16 and 20.
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