Question

The sum of the squares of two consecutive odd numbers is $394$. Find the numbers.

• A. $11,13$
• B. $13,15$
• C. $15,17$
• D. $17,19$

Answer 1

The correct option is B $13,15$

Let the Odd Consecutive Numbers be $2n+1,2n+3$

$(2n+1{)}^2+(2n+3{)}^2=394\Rightarrow 8n^2+16n+10=394\Rightarrow n^2+2n-48=0\Rightarrow (n-6)(n+8)=0\Rightarrow n=-8,6$

Now, $(2n+1,2n+3{)}_{atn=6}=(13,15\left)\right(2n+1,2n+3{)}_{atn=-8}=(-15,-13)$

So, the Numbers can be $(13,15)or(-13,-15)$