Question

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

Class 10

Quadratic Equation

Answer 1

Let the number be n^2. So

n^2 + n = 6/25, or

25 n^2 + 25 n = 6, or

25 n^2 + 25 n - 6 = 0

The product of 25 and -6 = -150. Its factors are +30 and -5. So we re-write the equation as

25 n^2 + 30 n - 5 n - 6 = 0, or

5n (5n +6) - 1*(5n + 6) = 0, or

(5n - 1)(5n +6) = 0

Therefore n = 1/5 or -6/5.

Check: 1/5 +(1/5)^2 = 1/5 + 1/25 = 6/25.

Also (-6/5) + (36/25) = (-30/25) + (36/25) = 6/25.

Answer 2

Let us assume the number as 'x^2'.

Given that sum of a number and its positive square root is 6/25.

⇒ x^2 + (√x^2) = 6/25

⇒ x^2 + x = 6/25

⇒ x^2 + x - 6/25 = 0

⇒ 25x^2 + 25x - 6 = 0

⇒ 25x^2 + 30x - 5x - 6 = 0

⇒ 5x(5x + 6) - (5x + 6) = 0

⇒ (5x - 1)(5x + 6) = 0

⇒ x = 1/5,-6/5{Neglect negative values}

⇒ x = 1/5

Then,

⇒ x^2 = 1/25.

Therefore, the number is 1/25.

Hope this helps!