[Toán 8] Chứng minh bất đẳng thức

I

i_am_challenger

[tex]bdt \Leftrightarrow 2x^2 + 2y^2 + 2z^2 - 2xy - 2yz - 2xz \geq0[/tex]
[tex]\Leftrightarrow (x^2 - 2xy + y^2) + (y^2 - 2yz + z^2)+(x^2 - 2xz + z^2)\geq0[/tex]
[tex]\Leftrightarrow (x-y)^2 + (y-z)^2 + (x-z)^2\geq0 \forall x \in R[/tex]
Vậy [tex]x^2 +y^2 +z^2 \geq xy+yz+xz [/tex]
 
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