c/m bdt

S

soicon_boy_9x

Câu 1:

$a^4+1+b^4+1 \ge 2a^2+2b^2 \ge 4ab$

Đẳng thức xảy ra khi $a=b=1$

Câu 2:

$a^4 \geq 4a-3 \leftrightarrow a^4-4a+3 \geq 0 \leftrightarrow a^4-a-3a+3
\ge 0 $

$\leftrightarrow a(a-1)(a^2+a+1)-3(a-1) \ge 0$

$\leftrightarrow (a-1)(a^3+a^2+a-3) \ge 0$

$\leftrightarrow (a-1)(a^3-a^2+2a^2-2a+3a-3) \ge 0$

$\leftrightarrow (a-1)^2(a^2+2a+3) \ge 0$( hiển nhiên đúng)

$\leftrightarrow dpcm$


 
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