Question

Fie a, b, c numere reale pozitive. Să se demonstreze că: b+c/a + a+c/b + a+b/c > sau egal cu 6 ..va rog, e urgent !​

Answer 1

Explicație pas cu pas:

a, b, c numere reale pozitive =>

$\frac{b}{a} + \frac{a}{b} \geqslant 2 \\ \frac{c}{b} + \frac{b}{c} \geqslant 2 \\ \frac{a}{c} + \frac{c}{a} \geqslant 2$

atunci:

$\frac{b + c}{a} + \frac{a + c}{b} + \frac{a + b}{c} = \frac{b}{a} + \frac{c}{a} + \frac{a}{b} + \frac{c}{b} + \frac{a}{c} + \frac{b}{c} = \\ = \Big(\frac{b}{a} + \frac{a}{b}\Big) + \Big(\frac{c}{b} + \frac{b}{c}\Big) + \Big(\frac{a}{c} + \frac{c}{a}\Big) \geqslant 2 + 2 + 2 = 6$

q.e.d.