Question

Demonstrati ca $x^{3} - \frac{1}{ x^{3} } \geq 3(x- \frac{1}{x} )$ oricare ar fi x∈ R, x≥1.

Answer 1

$(x- \frac{1}{x} )^{3}= x^{3}-3x^{2} \frac{1}{x} +3x \frac{1}{x^{2}} - \frac{1}{x^{3}} = x^{3} -3x+3 \frac{1}{x}- \frac{1}{x^{3}}$
Cum x≥1⇒$x- \frac{1}{x}$≥0 si rezulta ipoteza

Answer 2

Am rezolvat problema in fisierul atasat.