Question

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

• A. $11,13$
• B. $9,11$
• C. $13,15$
• D. $7,9$

Answer 1

The correct option is A $11,13$

Let the numbers be $x$ and $x+2$

$\therefore x^2+(x+2{)}^2=290$,

$2x^2+4x+4=290$

$x^2+13x-11x-143=0,$

$(x+13)(x-11)=0,$

$\therefore$ the numbers are $11$ and $13$