Question 964461
{{{A+B+17=40}}}
{{{A+B=23}}}
.
.
{{{A^2+B^2=17^2}}}
{{{(23-B)^2+B^2=289}}}
{{{B^2-46B+529+B^2=289}}}
{{{2B^2-46B+240=0}}}
{{{B^2-23B+120=0}}}
{{{(B-8)(B-15)=0}}}
Two solutions:
{{{B-8=0}}}
{{{B=8}}}
Then,
{{{A=23-8}}}
{{{A=15}}}
and
{{{B-15=0}}}
{{{B=15}}}
{{{A=8}}}