#### 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.

#### Solution

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

smallerpart = 2

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

Thus, the required number = 2 + 4 = 6

Is there an error in this question or solution?

Solution 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 P Concept: Quadratic Equations.