Tìm số đo góc ?

T

truongduong9083

Chào bạn

Ta có:
$p(p-a)(p-b)(p-c) \leq [\dfrac{3p - (a+b+c)}{3}]^3 = \dfrac{p^3}{27}$
$\Rightarrow p(p-a)(p-b)(p-c) \leq \dfrac{p^4}{27}$
$\Rightarrow S^2 \leq \dfrac{p^4}{27}$
$\Leftrightarrow 3\sqrt{3}S \leq p^2$
$\Leftrightarrow 12\sqrt{3}S \leq (a+b+c)^2$
Dấu "= " xảy ra khi $a = b= c$
hay tam giác ABC đều nhé
 
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