a-b-c-a-b-c-1-a-2-1-b-c-b-2-1-a-c-c-2-1-a-b-k-find-k-max-hint-inequality-cauchy-schwarz-

Question Number 205767 by lmcp1203 last updated on 30/Mar/24

a, b, c \in ℜ^{+}

a + b + c = 1

a^{2} / (1 + b + c) + b^{2} / (1 + a + c) + c^{2} / (1 + a + b) ⩾ k

f i n d k m a x .

h i n t : i n e q u a l i t y c a u c h y s c h w a r z

Answered by A5T last updated on 30/Mar/24

Σ \frac{a^{2}}{1 + b + c} ⩾ \frac{{(a + b + c)}^{2}}{3 + 2 (a + b + c)} = \frac{1}{5}

Commented by lmcp1203 last updated on 30/Mar/24

t h a n k s