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.
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 = 12Hence, the two numbers are 8 and 12.