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

1.	The sum of a number and its positive square root is 6/25. Find the number.
Answer» Given: The sum of a number and its positive square root is 6/25. To find: the number.Solution: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 factorise by splitting the middle term. ⇒ 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 only 1/25 is possible as its sum with its positive root is 6/25. Hence the number is 1/25.

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

Answer»

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

To find: the number.Solution: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

factorise by splitting the middle term.

⇒ 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 only 1/25 is possible as its sum with its positive root is 6/25.

Hence the number is 1/25.