Question

Find two consecutive odd positive integers, sum of whose squares is 970.

Answer 1

Let the two consecutive odd numbers be $x$ and $x+2.$
Given: sum of the squares of two consecutive odd positive integers is $970.$
According to question, we have

$x^2+(x+2{)}^2=970$

$\Rightarrow x^2+x^2+4x+4=970$

$\Rightarrow 2x^2+4x-966=0$

$\Rightarrow x^2+2x-483=0$

$\Rightarrow x^2+23x-21x-483=0$

$\Rightarrow x(x+23)-21(x+23)=0$

$\Rightarrow (x-21)(x+23)=0$

$\Rightarrow (x-21)=0or,(x+23)=0$

$\Rightarrow x=21or,x=-23$

Since the integers are positive so $x=21.$

Hence the other consecutive positive odd number is $21+2=23.$