Find two consecutive numbers whose squares have the sum of 85

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{6, 9}

{6, 10}

{6, 8}

{6, 7}

answer is D.

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Detailed Solution

Given, the sum of squares of two consecutive numbers is 85.
Say there be a number x.
The sum of the squares of x and (x+1) is 85.
The equation formed is,

x 2 + (x + 1) 2 = 85 ⇒ x 2 + x 2 + 2 x + 1 = 85 ⇒ 2 x 2 + 2 x − 84 = 0

⇒ x 2 + x − 42 = 0 ⇒ x 2 + 7 x − 6 x − 42 = 0 ⇒ x (x + 7) − 6 (x + 7) = 0 ⇒ (x − 6) (x + 7) = 0 ⇒ x = 6, (− 7)

So, the pair of numbers are:

{6, 6 + 1}

and

{(− 7), (− 7 + 1)},

that is

, {6, 7}, {− 7, − 6}

Two consecutive numbers whose squares have the sum of 85 are either

{6, 7}

{− 7, − 6}

So, the correct option is 4.

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