Question

The sum of the squares of two consecutive positive odd numbers is $290$. Find the sum of the numbers.

• A. $14$
• B. $24$
• C. $28$
• D. None

Answer 1

Answer: (B)

$24$

Let the smaller number be $x$.
Hence, $x^2+(x+2{)}^2=290$
$2x^2+4x+4=290$
$x^2+2x+2=145$
$x^2+2x-143=0$
$(x+1{)}^2-144=0$
$(x+1{)}^2={12}^2$
Since the numbers are positive,
$(x+1)=12$
$x=11$
Hence, the other number will be $13$.
Therefore, $13+11=24$.