Tìm giá trị lớn nhất

B

bongcan

$A= \frac{1}{x^2-2x.1/2+1/4+3/4}$
$ A= \frac{1}{(x-1/2)^2 +3/4}$
Vì $(x-1/2)^2$ \geq $0$ \forall$ x$
\Leftrightarrow $(x-1/2)^2 + 3/4$ \geq $3/4$ \forall $x$
\Leftrightarrow $\frac{1}{(x-1/2)^2 +3/4}$ \leq $\frac{1}{3/4}$
\Leftrightarrow $A$ \leq $4/3$
\Leftrightarrow $A min = 4/3$
dấu bằng xảy ra khi:
$x-1/2 = 0$
\Leftrightarrow $x=1/2$

~~> Lưu ý gõ tex
Thân~
 
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