[toán] bđt- cm

V

vuquynhthuhatinh

Last edited by a moderator:
H

hien_vuthithanh

1. $a^4 +1+1+1 \ge 4a$

$b^4+1+1+1 \ge 4b$

$\Longrightarrow a^4+b^4 \ge 4(a+b)-6=2$


2.$x^4+y^4+\dfrac{16}{9}+\dfrac{16}{9}\ge \dfrac{16}{3}xy$

$y^4+z^4+\dfrac{16}{9}+\dfrac{16}{9}\ge \dfrac{16}{3}yz$

$x^4+z^4+\dfrac{16}{9}+\dfrac{16}{9}\ge \dfrac{16}{3}zx$

$\Longrightarrow 2(x^4+y^4+z^4) \ge \dfrac{16}{3}(xy+yz+zx)-6.\dfrac{16}{9}=\dfrac{32}{3}$

$\Longrightarrow x^4+y^4+z^4 \ge \dfrac{16}{3}$
 
L

lp_qt

Câu 1:

$a^4+b^4 \ge \dfrac{(a^2+b^2)^2}{2} \ge \dfrac{\left ( \dfrac{(a+b)^2}{2} \right )^2}{2}=2$

Câu 2:

$x^4+y^4+z^4 \ge x^2y^2+y^2z^2+x^2z^2 \ge \dfrac{(xy+yz+xz)^2}{3}=\dfrac{16}{3}$
 
You must log in or register to reply here.
Top Bottom