Question

Find the two consecutive positive integers, such that their sum of whose squares is 365.

• A. 17, 18
• B. 13, 14
• C. 9, 10
• D. 12, 13

Answer 1

The correct option is B

13, 14

Let the numbers be x and x+1

$x^2$+$(x+1{)}^2$=365

$\Rightarrow$ $x^2$+$x^2$+2x+1=365

$\Rightarrow$2$x^2$+2x-364=0

$\Rightarrow$ $x^2$+x-182=0(on dividing by 2)

$\Rightarrow$ $x^2$+14x-13x-182=0

$\Rightarrow$ x =13 or -14 .

Therefore, x = 13 [positive integers are considered in the problem]

So, required consecutive numbers are 13 and 14.