Question 39164
{{{x + y = 25}}}
{{{x^2 + y^2 = 313}}}
Simplify:
{{{x^2 + y^2 = 313}}}
{{{x^2 = 313 - y^2}}}
{{{x = sqrt(313 - y^2)}}}
Plug in:
{{{x + y = 25}}}
{{{sqrt(313 - y^2) = 25 - y}}}
{{{313 - y^2 = y^2 - 50y + 625}}}
{{{313 = 2y^2 - 50y + 625}}}
{{{0 = y^2 - 25y + 156}}}
{{{0 = (y - 13)(y - 12)}}}
{{{y = 13}}} or {{{y = 12}}}
Plug in:
{{{x + y = 25}}}
{{{x + 13 = 25}}}
{{{x = 12}}}
and
{{{x + y = 25}}}
{{{x + 12 = 25}}}
{{{x = 13}}}
The numbers are twelve and thirteen.