Giải thích các bước giải:

Câu 27:

Ta có:

$\dfrac14x^2+(\dfrac12x-y)^2+(\dfrac12x-z)^2+(\dfrac12x-t)^2\ge 0$

$\Leftrightarrow x^2+y^2+z^2+t^2-xy-xz-xt\ge 0$

$\Leftrightarrow x^2+y^2+z^2+t^2\ge xy+xz+xt$

$\Leftrightarrow x^2+y^2+z^2+t^2\ge x(y+z+t)$

Câu 28:

Ta có:

$\dfrac1a+\dfrac1b+\dfrac1c=\dfrac{1^2}a+\dfrac{1^2}b+\dfrac{1^2}c\ge\dfrac{(1+1+1)^2}{a+b+c}=\dfrac9{a+b+c}$

$\Leftrightarrow \dfrac{ab+bc+ca}{abc}\ge\dfrac9{a+b+c}$

$\Leftrightarrow (a+b+c)(ab+bc+ca)\ge 9abc$

$\Leftrightarrow đpcm$