1. Three consecutive natural numbers are such that the square of the greatest is greater than the product of the other two by 16. The smallest of these numbers is
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By: anil on 05 May 2019 02.13 am
Let the three consecutive natural numbers be $$(x-1) , (x) , (x+1)$$ where $$x geq 2$$ Acc. to ques, => $$(x + 1)^2 - [x imes (x - 1)] = 16$$ => $$(x^2 + 2x + 1) - (x^2 - x) = 16$$ => $$3x + 1 = 16$$ => $$x = frac{15}{3} = 5$$ $$ herefore$$ Smallest number = 5 - 1 = 4
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