[Toán 8]Chứng minh bất đẳng thức

C

chonhoi110

$M = 4x(x +y)(x + y + z)(x + z) + y^2z^2$

$ = 4(x^2 + xy + xz)(x^2 + xy + xz + yz) + y^2z^2$

Đặt $x^2 + xy + xz = a$

$\rightarrow M = 4a(a + yz) + y^2z^2$

$= 4a^2 - 4ayz + (yz)^2$

$= (2a + yz)^2$
$\rightarrow (Q.E.D)$
 
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