Question

The sum of a natural number and its square is 156. Find the number.​

Answer 1

Given:-

The sum of a natural number and its square is 156.

To Find:-

The number.

Formula to be used:-

Splitting middle term

Comparing the given equation with ax² + bx + c = 0

Solution:-

Let the required number be x.

According to the Question,

⇒ x² + x - 156 = 0

⇒ x² + 13x - 12x - 156 = 0

⇒ x(x + 13) - 12 (x + 13) = 0

⇒ (x - 12) (x + 13) = 0

⇒ x - 12 = 0 or x + 13 = 0

⇒ x = 12, - 13 (As x can't be negative)

⇒ x = 12

Hence, the required natural number is 12.

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