Question
Sat July 21, 2012 By: Janani S

A positive number is divided into two parts such that the sum of the squares of the two parts is 208.The square of the larger part is 8 times the smaller part. Taking 'x' as the smaller part, find the number.

Expert Reply
Sun July 22, 2012

Let the two numbers be x and y, y being the bigger number. From the given information,

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 = 12

Hence, the two numbers are 8 and 12.
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