Giải phương trình

L

lp_qt

1.

$\sqrt{2x-1}\le \dfrac{2x-1+1}{2}=x$

$\sqrt{2-x^2}\le \dfrac{2-x^2+1}{2}=\dfrac{3-x^2}{2}$

\Rightarrow $\sqrt{2x-1}+\sqrt{2-x^2}\le x+\dfrac{3-x^2}{2}=\dfrac{-x^2+2x+3}{2}=\dfrac{-(x+1)^2+4}{2}\le 2$

dấu bằng xảy ra \Leftrightarrow $x=1$
 
D

dien0709

$ 2) log_3 (2x) = log_2 (\dfrac{3}{x^2}) $

\Rightarrow $ log_32 + log_3x = log_23 - 2log_2x $ \Rightarrow $ log_23 - log_32 = log_3x+2log_2x $

= $ log_32.log_2x + 2log_2x $= $ log_2x(log_32+2) $

\Rightarrow $ log_2x = \dfrac{log_23 - log_32}{log_32 + 2}$ = a

\Rightarrow $ x = 2^a $
 
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