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

Question

Philoid · Accepted Answer

Let the number be ‘a’.

⇒ a + √a = 6/25

⇒ √a = (6/25) – a

Squaring both sides

⇒ a = 36/625 + a² – 12a/25

⇒ a² – 37a/25 + 36/625 = 0

⇒ a² – a/25 – 36a/25 + 36/625 = 0

⇒ a(a – 1/25) – (36/25) × (a – 1/25) = 0

⇒ (a – 36/25)(a – 1/25) = 0

⇒ a = 36/25 , 1/25

But 1/25 as its sum with its positive root is 6/25