Rút gọn, tìm x

V

vipboycodon

a) $B = \dfrac{\sqrt{x}(\sqrt{x^3}+1)}{x-\sqrt{x}+1}+\dfrac{\sqrt{x}-(2x+\sqrt{x})}{\sqrt{x}}$

$B = \dfrac{\sqrt{x}(\sqrt{x}+1)(x-\sqrt{x}+1)}{x-\sqrt{x}+1}-\dfrac{2x}{\sqrt{x}}$

$B = \sqrt{x}(\sqrt{x}+1)-2\sqrt{x}$

$B = x-\sqrt{x}$

b) Để B = 2 => $x-\sqrt{x} = 2$
<=> $x-\sqrt{x}-2 = 0$

<=> $(\sqrt{x}-2)(\sqrt{x}+1) = 0 $

<=> $x = 4$

c) $B = x-\sqrt{x}$

= $x-2\sqrt{x}\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{4}$

= $(\sqrt{x}-\dfrac{1}{2})^2-\dfrac{1}{4} \ge \dfrac{-1}{4}$
 
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