Răspuns:
[tex] \frac{ {a}^{2} + {b}^{2} }{a + b} \geqslant \frac{a + b}{2} [/tex]
[tex]( {a}^{2} + {b}^{2} ) \times 2 \geqslant {(a + b)}^{2} [/tex]
[tex]2 \times {a}^{2} + 2 \times {b}^{2} \geqslant {a}^{2} + 2 \times a \times b + {b}^{2} [/tex]
[tex] {a}^{2} + {b }^{2} - 2ab \geqslant 0[/tex]
[tex]{(a - b)}^{2} \geqslant 0 = > a.b > 0[/tex]
