Question

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

Answer 1

Let one of the number be x then other number is x + 2.

Then according to question,

$$\begin{gathered} x^2+{\left(x+2\right)}^2=970 \\ \Rightarrow x^2+x^2+4x+4=970 \\ \Rightarrow 2x^2+4x-966=0 \\ \Rightarrow x^2+2x-483=0 \\ \Rightarrow x^2+23x-21x-483=0 \\ \Rightarrow x(x+23)-21(x+23)=0 \\ \Rightarrow (x-21)(x+23)=0 \\ \Rightarrow x-21=0\mathrm{or}x+23=0 \\ \Rightarrow x=21\mathrm{or}x=-23 \end{gathered}$$

Since, x being an odd positive integer,

Therefore, x = 21.

Then another number will be

$x+2=21+2=23$

Thus, the two consecutive odd positive integers are 21 and 23.