Question

The sum of the squares of two consecutive positive integers is $545$. Find the sum of these integers.

• A. $33$
• B. $434$
• C. $35$
• D. $36$

Answer 1

Answer: (A)

$33$

Let one integer be $x$, hence another will be $x+1$.
Hence
$x^2+(x+1{)}^2=545$
$2x^2+2x-544=0$
$x^2+x-272=0$
$(x-16)(x+17)=0$
Now the numbers are positive.
$\therefore x=16$
Therefore the other number will be 17.

Then sum of the two integers $=16+17=33$