Question 44

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

Solution

Let the three consecutive natural numbers be $$(x-1) , (x) , (x+1)$$ where $$x \geq 2$$

Acc. to ques, => $$(x + 1)^2 - [x \times (x - 1)] = 16$$

=> $$(x^2 + 2x + 1) - (x^2 - x) = 16$$

=> $$3x + 1 = 16$$

=> $$x = \frac{15}{3} = 5$$

$$\therefore$$ Smallest number = 5 - 1 = 4

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