Question

A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.

Answer 1

Let the smaller part be x

Then, (larger part)² = 8x

∴ Larger part = `sqrt(8x)`

Now, the sum of the squares of both the terms is given to be 20

`x^2 + (sqrt(8x))^2 = 20`

`⇒ x^2 + 8x = 20`

`=> x^2 + 8x - 20 = 0`

`=> x^2 - 2x + 10x - 20 = 0`

`=> x(x - 2) + 10(x - 2) = 0`

`=> (x - 2)(x + 10) = 0`

`=> x = 2 or x = -10`

x = –10 is rejected as it is negative

∴ x = 2

Smaller part = 2

Larger part = `sqrt(8 xx 2)` = 4

Thus, the required number = 2 + 4 = 6