if-a-b-c-lt-0-and-a-b-c-3-prove-that-1-b-a-1-b-2-1-c-b-1-c-2-1-a-c-1-a-2-8-

Question Number 164416 by HongKing last updated on 16/Jan/22

if a; b; c < 0 and a + b + c = 3 prove that :

{(1 + \frac{b}{a})}^{\frac{1}{b^{2}}} \cdot {(1 + \frac{c}{b})}^{\frac{1}{c^{2}}} \cdot {(1 + \frac{a}{c})}^{\frac{1}{a^{2}}} ⩾ 8