Question 150

If the product of two successive positive integers is 3192, which is the smaller integer?

Solution

Let the two successive positive integers be $$(x)$$ & $$(x + 1)$$

Acc to ques,

=> $$(x) \times (x + 1) = 3192$$

=> $$x^2 + x - 3192 = 0$$

=> $$x = \frac{-1 \pm \sqrt{(1^2) - (4 \times 1 \times -3192)}}{2}$$

=> $$x = \frac{-1 \pm \sqrt{21769}}{2}$$

=> $$x = \frac{-1 \pm 113}{2}$$

=> $$x = 56 , -57$$

Since the numbers are positive, => $$x = 56$$

$$\therefore$$ Smaller number = 56

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