Explicație pas cu pas:
[tex]f(a) + f\Big( \frac{1}{a} \Big) = {a}^{2} + a + 1 + \frac{1}{ {a}^{2} } + \frac{1}{a} + 1 \\ [/tex]
[tex]= {a}^{2} + 2 \cdot a \cdot \frac{1}{2} + \frac{1}{4} + \frac{3}{4} + \frac{1}{ {a}^{2} } + 2 \cdot \frac{1}{a} \cdot \frac{1}{2} + \frac{1}{4} + \frac{3}{4} \\ [/tex]
[tex]= {\Big(a + \frac{1}{2} \Big)}^{2} + {\Big( \frac{1}{a} + \frac{1}{2} \Big)}^{2} + \frac{3}{2} \geqslant \frac{3}{2} \\ [/tex]
q.e.d.
