Question

The sum of natural number and its square is 113 ,Find the number.​

Answer 1

Answer:

10 is the natural number.

Step-by-step explanation:

I THINK THAT 113 IS A TYPO. IT SHOULD BE 110 AS THERE IS NO NATURAL NO. THAT ADDS UP WITH ITS SQUARE TO BECOME 113. SO I AM GOING TO TAKE THE SUM AS 110.

Let the natural no. be x.

So, acc. to ques, x + x² = 110

=> x² + x - 110 = 0

=> x² - 11x + 10x - 110 = 0

=> x(x - 11) + 10(x - 11) = 0

=> (x - 11)(x + 10) = 0

∴ x = 10, -11

As -11 isn't a natural number, x = 10 is the answer.

Answer 2

Step-by-step explanation:

Let the two consecutive natural numbers be x and x + 1

As per the given condition,

x2 + (x + 1)2 = 113

∴ x2 + x2 + 2x + 1 = 113

∴ 2x2 + 2x + 1 – 113 = 0

∴ 2x2 + 2x – 112 = 0

Dividing by 2 we get,

x2 + x – 56 = 0

∴ x2 + 8x – 7x – 56 = 0

∴ x (x + 8) – 7 (x + 8) = 0

∴ (x + 8) (x – 7) = 0

∴ x + 8 = 0 or x – 7 = 0

∴ x = – 8 or x = 7

∵ x is a natural number

∴ x cannot be negative

∴ x = 7

And x + 1 = 7 + 1 = 8

∴ The two consecutive natural numbers are 7 and 8

respectively