Χαράλαμπος .Σπ. Λυκούδης - ΜαθηματικόςΜαθηματικό Στέκι…Κατασκευαστής Σελίδας: Χαρ. Λυκούδης
\boldsymbol{\color{Blue} \Delta\acute{i}\delta o\nu\tau\alpha\iota \:\: o\iota \:\: \pi\rho\alpha\gamma\mu\alpha\tau\iota\kappa o\acute{i} \:\: \alpha\rho\iota\theta\mu o\acute{i} \:\:\:\ a, x, y \in IR \:\:\:\: \gamma\iota\alpha \: \tau o \upsilon s \: o\pi o\acute{i} o \upsilon s \: \epsilon\acute{i}\nu\alpha\iota:}
\boldsymbol{\color{Blue}\ 2a-2x+y\geq 0 \:\:\:\:\:\:\:\:\:\:\:\: \kappa\alpha\iota\:\:\:\:\:\:\:\:\:\:\:\: 4a-x\leq 0\:\:\:\:\:\:\:\:(1).}
\boldsymbol{\color{Blue} N\alpha \,\,\, \delta\epsilon\acute{\iota}\xi\epsilon\tau\epsilon \:\: \acute{o}\tau\iota: }
\boldsymbol{\color{Blue} \ 6a^2+2x^2-10ax+4ay-xy+3x-2y\leq 0 \:\:\:\:\:\:\:\: (2). }
\boldsymbol{\color{Black} \Lambda\acute{\upsilon}\sigma\eta}
\boldsymbol{\color{Blue} \Sigma\acute{\upsilon}\mu\phi\omega\nu\alpha \,\,\, \mu\epsilon \,\,\, \tau\alpha \,\,\, \delta\epsilon\delta o \mu\acute{\epsilon}\nu\alpha \,\,\, \epsilon\acute{\iota}\nu\alpha\iota: \,\,\, \left \{\begin{matrix} 2a-2x+y \geq 0 \\ \kappa\alpha\iota \\4a-x \leq 0 \end{matrix} \right\}.}
\boldsymbol{\color{Blue} \Theta\acute{\epsilon}\tau o\upsilon\mu\epsilon: }
\boldsymbol{\color{Blue} \left \{\begin{matrix} 2a-2x+y=\theta_1 \\ \kappa\alpha\iota \\4a-x =-\theta_2 \end{matrix} \right\}\:\:\:\: \mu\epsilon \:\:\:\: \theta_1, \:\: \theta_2 \geq 0 \Leftrightarrow \cdots \Leftrightarrow \left \{\begin{matrix} x=4a+\theta_2 \\ \kappa\alpha\iota \\y=6a+\theta_1+2\theta_2 \end{matrix} \right\} \:\:\:\:\:\:\:\:(3).}
\boldsymbol{\color{Blue} To \,\,\, \pi\rho\acute{\omega}\tau o \,\,\, \mu\acute{\epsilon}\lambda o\varsigma \,\,\, \tau\eta\varsigma \,\,\, \alpha\pi o\delta\epsilon\iota\kappa\tau\acute{\epsilon}\alpha\varsigma \,\,\, \sigma\chi\acute{\epsilon}\sigma\eta\varsigma \,\,\, (2) \,\,\, \mu\epsilon\tau\alpha \,\,\, \tau\eta\nu \,\,\, \alpha\nu\tau\iota\kappa\alpha\tau\acute{\alpha}\sigma\tau\alpha\sigma\eta }
\boldsymbol{\color{Blue} \tau\omega\nu \,\,\, x, \,\, y \,\,\, \alpha\pi o \,\, \tau\iota\varsigma \,\, \iota\sigma\acute{o}\tau\eta\tau\epsilon\varsigma \,\,\,(3) \,\,\, \kappa\alpha\iota \,\,\, \tau\eta\nu \,\,\, \epsilon\kappa\tau\acute{\epsilon}\lambda\epsilon\sigma\eta \,\,\, \tau\omega\nu \,\,\, \pi\rho\acute{\alpha}\xi\epsilon\omega\nu \,\,\, \gamma\rho\acute{\alpha}\phi\epsilon\tau\alpha\iota:}
\boldsymbol{\color{Blue} 6a^2+2x^2-10ax+4ay-xy+3x-2y =\cdots=}
\boldsymbol{\color{Blue} =-(2a^2+\theta_1\theta_2+\theta_2+2\theta_1) \leq 0 \:\:\:\:\:\:\:\:(4).}
\boldsymbol{\color{Blue} H \,\, \iota\sigma\acute{o}\tau\eta\tau\alpha \,\, \sigma\tau\eta\nu \,\, \alpha\pi o\delta\epsilon\iota\kappa\tau\acute{\epsilon}\alpha \,\, \sigma\chi\acute{\epsilon}\sigma\eta \,\,\, (2) \,\,\, \iota\sigma\chi\acute{\upsilon}\epsilon\iota, \,\,\,\acute{o}\tau\alpha\nu \,\, \iota\sigma\chi\acute{\upsilon}\epsilon\iota \,\, \eta \,\, \iota\sigma\acute{o}\tau\eta\tau\alpha \,\, \sigma\tau\eta\nu \,\,\, }
\boldsymbol{\color{Blue} (4), \,\,\, \delta\eta\lambda\alpha\delta\acute{\eta} \,\, \acute{o}\tau\alpha\nu: }
\boldsymbol{\color{Blue} \left \{\begin{matrix} a=0, \:\:\: \theta_1=0 \:\:\: \kappa\alpha\iota \:\:\: \theta_2=0 \end{matrix} \right\} \Leftrightarrow \left \{\begin{matrix} a=0, \:\:\: x=0 \:\:\: \kappa\alpha\iota \:\:\: y=0 \end{matrix} \right\}.}