Question

A positive number is divided into two parts such that the sum of two parts is 208. The square of the larger part is 88 times the smaller part, find the number.

Answer 1

Answer:

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.