x+y=5,⇒ x =5 - y
xy=6 ⇒ (5 - y) × y =6⇒ 5y - y² = 6
6+y²-5y =0
y²-5y+6=0
Δ=25-24=1
y₁=(5+1)/2=3⇒ x₁=2
y₂=(5-1)/2=2⇒ x₂=3
deci y₁ = 3⇒ x₁= 2 si y₂ = 2⇒ x₂ = 3
a) (x+y)²=(3+2)²=5²=25
b)
x²+y²=13
2²+3²=4+9=13
c)y₁ = 3⇒ x₁= 2 si y₂ = 2⇒ x₂ = 3
a=(x-y)² +1/x + 1/y =(2-3)²+1/2+1/3=1+1/2+1/3=(6+2+3)/6=11/6
a= (3-2)²+1/3+1/2=1+1/3+1/2=11/6
[tex] \it x+y=5\ \ \ \ (1)
\\ \\ \\
xy = 6 \ \ \ \ \ \ \ \ (2)
\\ \\ \\
a)\ (x+y)^2\ \stackrel{(1)}{=} \ 5^2 = 25 \ \ \ \ \ \ (3)
\\ \\ \\
b)\ x^2+y^2 = (x+y)^2 -2xy \ \stackrel{(3), (2)}{=} \ 25-2\cdot6 =25-12=13.
[/tex]
[tex] \it c)\ (x-y)^2 +\dfrac{1}{x} +\dfrac{1}{y} = (x+y)^2 -4xy ++\dfrac{x+y}{xy} = 25 - 4\cdot6+\dfrac{5}{6} = 1+\dfrac{5}{6}=
\\ \\ \\
= \dfrac{11}{6} [/tex]