Let the natural number be x.

According to the question,

x + 12 = \( \dfrac{160}{x}\)

On multiplying by x on both sides, we get

⇒ x^{2} + 12x – 160 = 0

⇒ x^{2} + (20x – 8x) – 160 = 0

⇒ x^{2} + 20x – 8x – 160 = 0 [by factorisation method]

⇒ x (x + 20) – 8 (x + 20) = 0

⇒ (x + 20) (x – 8) = 0

Now, x + 20 = 0 ⇒ x = -20 which is not possible because natural number is always greater than zero

and x – 8 = 0 ⇒ x = 8.

Hence, the required natural number is 8.

Answered by Aaryan | 9 months agoFind a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.

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