Resolva os sistemas {x2+y2=169 {x+y=17

No problema em questão, temos que:

\[\eqalign{ & x + y = 17 \cr & x = 17 - y \cr & \cr & {x^2} + {y^2} = 169 \cr & {\left( {17 - y} \right)^2} + {y^2} = 169 \cr & 289 - 34y + {y^2} + {y^2} = 169 \cr & 2{y^2} - 34y + 120 = 0 \cr & \cr & a = 2 \cr & b = - 34 \cr & c = 120 \cr & \cr & y = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}} \cr & = \dfrac{{ - \left( { - 34} \right) \pm \sqrt {{{\left( { - 34} \right)}^2} - 4 \cdot 2 \cdot 120} }}{{2 \cdot 2}} \cr & \cr & y' = 12 \cr & y'' = 5 \cr & \cr & x' = 5 \cr & x'' = 12 }\]