Q. 104.3( 12 Votes )

# The sum of a numb

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.

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