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Question
The sum of the square of 2 positive integers is 208. If the square of larger number is 18 times the smaller number, find the numbers.
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Solution
Let these two numbers be X and Y, Y being the bigger number. Then as per the question,
X2+Y2= 208 ..... (i)
Y2 = 18X ..... (ii)
From (i), we get Y2= 208 - X2. Putting this in (ii), we get
208 - X2 = 18X
⇒ x2 + 18X - 208 = 0
⇒ X2 + 26X - 8X - 208 = 0
⇒ X(X + 26) - 8(X + 26) = 0
⇒ (X-8) (X+ 26) = 0
⇒ X can't be a negative number , hence X=8
⇒ Putting X=8 in (ii), we get Y2 = 18 x 8=144
⇒ Y= l 2
⇒ X=8 and Y = 12.
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