Sendo x+y=5 e x.y=8, então x2+y2 é igual a:

\[\eqalign{ & \left( {x + y} \right) = 5 \cr & {\left( {x + y} \right)^2} = {5^2} \cr & {x^2} + 2xy + {y^2} = 25 \cr & {x^2} + {y^2} + 2 \cdot \left( {x \cdot y} \right) = 25 \cr & {x^2} + {y^2} + 2 \cdot 8 = 25 \cr & {x^2} + {y^2} + 16 = 25 \cr & {x^2} + {y^2} = 25 - 16 \cr & {x^2} + {y^2} = 9 }\]

Portanto, resulta que \(\boxed{{x^2} + {y^2} = 9}\).

x + y)2 = x2 + 2.x.y + y2

x + y = 5   e x.y = 8

( x + y )2 = 52

x2 + 2.x.y + y2 = 25

x2 + y2 = 25 - 2.x.y

x2 + y2 = 25 - 2.(8)

x2 + y2 = 25 - 16

x2 + y2 = 9

R: 9

(x+y)² = 5²

x²+2xy+y² = 25

x²+y² = 25-2xy

x²+y² = 25-16 = 9