Question

Express the following as the sum of two consecutive positive integers.

i) ${15}^2$

ii) ${21}^2$

Answer 1

i) Let us consider the consecutive positive integers be $x,x+1$.

According to the problem,

$x+(x+1)={15}^2$

or, $2x+1=225$

or, $2x=224$

or, $x=112$.

The required integers are $112,113$.

ii) Let us consider the consecutive positive integers be $x,x+1$.

According to the problem,

$x+(x+1)={21}^2$

or, $2x+1=441$

or, $2x=440$

or, $x=220$.

The required integers are $220,221$.