1.

If the sum of the square of 2 positive consecutive integers is 3445.Then, find the sum of the numbers.1. 862. 783. 984. 83

Answer» Correct Answer - Option 4 : 83

Let the two consecutive integers are x and (x + 1)

According to question

(x)2 + (x + 1)2 = 3445

⇒ x2 + x2 + 1 + 2x = 3445

⇒ 2x2 + 2x + 1 = 3445

⇒ 2x2 + 2x – 3444 = 0

⇒ x2 + x – 1722 = 0

Using D = b2 - 4ac

= (1)2 - 4(1)(-1722)

= 6889

x = (- b + √D)/2a, or (-b - √D)/2a

⇒ (- 1 + √6889)/2(1), or (- 1 - √6889)/2(1)

⇒ (- 1 + 83)/2, or -1 – 83/2

⇒ 82/2, or -84/2

⇒ 41, or -42

x is not negative, therefore the positive numbers are 41 and 42 i.e. (41 + 1)

∴ Sum of the numbers is 83


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