Question 41589
Equation:
{{{y^2 + x^2 = 130}}}
{{{y^2 = 130 - x^2}}}
{{{y = sqrt(130 - x^2)}}}
Other Equation:
{{{y = x + 8}}}
Plug:
{{{y = x + 8}}}
{{{sqrt(130 - x^2) = x + 8}}}
{{{130 - x^2 = x^2 + 16x + 64}}}
{{{0 = 2x^2 + 16x - 66}}}
{{{0 = x^2 + 8x - 33}}}
{{{0 = x^2 + 11x - 3x - 33}}}
{{{0 = (x^2 + 11x) + (-3x - 33)}}}
{{{0 = x(x + 11) - 3(x + 11)}}}
{{{0 = (x - 3)(x + 11)}}}
{{{x = 3}}} and {{{x = -11}}}
Plug:
{{{y^2 + 3^2 = 130}}}
{{{y^2 + 9 = 130}}}
{{{y^2 = 121}}}
{{{y = 11}}} or {{{y = -11}}}
The numbers are three and eleven.