Question

The sum of a numbers and its positive square root is `6/25`. Find the numbers.

Answer 1

Let the number be x

By the hypothesis, we have

`rArrx+sqrtx=6/25`

⇒ let us assume that x = y², we get

`rArry^2+y=6/25`

⇒ 25𝑦² + 25𝑦 − 6 = 0

The value of ‘y’ can be obtained by

`y=(-b+-sqrt(b^2-4ac))/(2a)`

Where a = 25, b = 25, c = −6

`rArry=(-25+-sqrt(625-600))/50`

`rArry=(-25+-25)/50`

`rArry=1/5` or `-11/10`

`x=y^2=(1/5)^2=1/25`

∴ The number x = `1/25`