Question

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

• A. 16, 17
• B. 15, 16
• C. 14, 15
• D. None of these

Answer 1

The correct option is A 16, 17

Let one positive integer be $x$
$\therefore$ Other positive integer will be $x+1$
${\left(x\right)}^2+{(x+1)}^2=545$
$x^2+x^2+1+2x=545$
$2x^2+2x-544=0$
$x^2+x-272=0$
$x^2+17x-16x-272=0$
$x(x+17)-16(x+17)=0$
$(x-16)(x+17)=0$
$\therefore x=16$ or $x=-17$ (Not Possible)
So, consecitive integers are 16 and 17