The sum of the squares of two positive integers is 208 If the square of the larger number is 18 time...........

Quantitative Aptitude (CDS) Number System

The sum of the squares of two positive integers is 208.If the square of the larger number is 18 times the smaller number, then what is the difference of the larger and smaller numbers?

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Explanation:

Let two positive integers be x and yysuch that x>y
According to question,
x²+y²=208 ……. (i)
x²=18y……. (ii)
From (i) and (ii)
y²+18y−208=0
=> (y+26)(y−8)=0
=> y=−26 or y=8
As, x²=18y
If y=−26
Then x²=18×(−26) [Not possible]
If y=8
Then x2=18×8=144
=> x =12
Then x −y =12−8=4
Hence option (3)