Question

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Answer 1

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Answer 2

Explicație pas cu pas:

$f(a) + f\Big( \frac{1}{a} \Big) = {a}^{2} + a + 1 + \frac{1}{ {a}^{2} } + \frac{1}{a} + 1$

$= {a}^{2} + 2 \cdot a \cdot \frac{1}{2} + \frac{1}{4} + \frac{3}{4} + \frac{1}{ {a}^{2} } + 2 \cdot \frac{1}{a} \cdot \frac{1}{2} + \frac{1}{4} + \frac{3}{4}$

$= {\Big(a + \frac{1}{2} \Big)}^{2} + {\Big( \frac{1}{a} + \frac{1}{2} \Big)}^{2} + \frac{3}{2} \geqslant \frac{3}{2}$

q.e.d.