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

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08 Oct 2010 Find the number

The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller,
find the smaller number.

OPtion

1) 1
2) 22
3) 3
4) 4
5) 15
6) 6
7) 8
8) 7
9) 10
10) 12

Solution

Let two postive numbers be x & y and x > y
X^2 + Y^2 = 208 .....................................(i)
X^2 = 18y ................................................(ii)

Y^2 + 18y - 208 = 0
=>(y+26) ( y-8)=0
=> y= -26 or y =8
Putting Y = 8 in (ii) X = 12, X= -12 (false)
X = 12, Y = 8

Correct Option: 7 Best Solution (0)