Question

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

• A. $13,15$
• B. $15,17$
• C. $11,13$
• D. None of these

Answer 1

The correct option is C $11,13$

Let the two consecutive odd integers be $x$ and $(x+2)$.

Then the equation we get is equal to
$x^2+(x+2{)}^2=290$
$\Rightarrow x^2+x^2+4x+4-290=0$
$\Rightarrow 2x^2+4x-286=0$
$\Rightarrow x^2+2x-143=0$
$\Rightarrow x^2+13x-11x-143=0$
$\Rightarrow x(x+13)-11(x+13)=0$
$\Rightarrow (x+13)(x-11)=0$
$\Rightarrow x=-13$ or $x=11$
Here,$-13$ is not an odd positive integer.

Hence, the required integers are $11,13$.