A natural number when increased by 12, equals 160 times reciprocal. The number is-
Created: 1 year ago |
Updated: 10 months ago
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Step 1: Construct the equation based on given condition.
let the required natural number be x.
According to the question,
x+12=160/x
On multiplying by x on both sides, we get
x^2+12x−160=0,
step 2: Find roots using factorization.
By splitting the middle term, we get :
⇒x^2+(20x−8x)−160=0
⇒x^2+20x−8x−160=0
⇒x(x+20)−8(x+20)=0
⇒(x+20)(x−8)=0
⇒x=8
[x≠−20 because it is not a natural number]
hence, the required natural number is 8
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