Let the natural number be x.
According to the question,
x + 12 = \( \dfrac{160}{x}\)
On multiplying by x on both sides, we get
⇒ x2 + 12x – 160 = 0
⇒ x2 + (20x – 8x) – 160 = 0
⇒ x2 + 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.
The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is \( \dfrac{29}{20}\) Find the original fraction.
The sum of the squares of two consecutive even numbers is 340. Find the numbers.
The sum of the squares of two consecutive multiple of 7 is 637. Find the multiples.
The sum of the squares of two consecutive odd numbers is 394. Find the numbers.