Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.

Asked by Sakshi | 9 months ago |  121

##### Solution :-

Let n be a required natural number.

Square of a natural number diminished by 84 = n2 – 84

and thrice of 8 more than the natural number = 3 (n + 8)

Now, by given condition,

n2 – 84 = 3 (n + 8)

⇒ n2 – 84 = 3n + 24

⇒ n2 – 3n – 108 = 0

⇒ n2 – 12n + 9n – 108 = 0 [by splitting the middle term]

⇒ n (n – 12) + 9 (n – 12) = 0

⇒ (n – 12) (n + 9) = 0

⇒ n = 12 [n ≠ – 9 because n is a natural number

Answered by Aaryan | 9 months ago

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