Question 202155
Let n = the required number, so...
{{{(n+3)^2 = (n+2)^2+13}}} Expand.
{{{n^2+6n+9 = n^2+4n+4+13}}} Subtract {{{n^2}}} from both sides.
{{{6n+9 = 4n+17}}} Subtract 4n from both sides.
{{{2n+9 = 17}}} Subtract 9 from both sides.
{{{2n = 8}}} Finally, divide both sides by 2.
{{{highlight(n = 4)}}}
Check:
{{{(n+3)^2 = (n+2)^2+13}}} Substitute n = 4.
{{{(4+3)^2 = (4+2)^2+13}}} Evaluate.
{{{49 = 36+13}}}
{{{49 = 49}}} OK!