Cho P=1/2√x-2-1/2√x+2-√x/x-1
a, tìm dkxd b, rút gọn. C, tính P khi x=4/9. d, tìm x để |P| = 1/3
Cho P=1/2√x-2-1/2√x+2-√x/x-1
a, tìm dkxd b, rút gọn. C, tính P khi x=4/9. d, tìm x để |P| = 1/3
Đáp án:
$\begin{array}{l}
a)Dkxd:x \ge 0;x \ne 1\\
b)P = \dfrac{1}{{2\sqrt x – 2}} – \dfrac{1}{{2\sqrt x + 2}} – \dfrac{{\sqrt x }}{{x – 1}}\\
= \dfrac{{\sqrt x + 1 – \left( {\sqrt x – 1} \right) – 2\sqrt x }}{{2\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}\\
= \dfrac{{2 – 2\sqrt x }}{{2\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}\\
= \dfrac{{ – 2\left( {\sqrt x – 1} \right)}}{{2\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}\\
= \dfrac{{ – 1}}{{\sqrt x + 1}}\\
c)x = \dfrac{4}{9}\left( {tmdk} \right)\\
\Rightarrow \sqrt x = \dfrac{2}{3}\\
\Rightarrow P = \dfrac{{ – 1}}{{\sqrt x + 1}} = \dfrac{{ – 1}}{{\dfrac{2}{3} + 1}} = \dfrac{{ – 3}}{5}\\
d)\left| P \right| = \dfrac{1}{3}\\
\Rightarrow P = \dfrac{{ – 1}}{3}\left( {do: – \dfrac{1}{{\sqrt x + 1}} < 0} \right)\\
\Rightarrow – \dfrac{1}{{\sqrt x + 1}} = – \dfrac{1}{3}\\
\Rightarrow \sqrt x + 1 = 3\\
\Rightarrow \sqrt x = 2\\
\Rightarrow x = 4\left( {tmdk} \right)
\end{array}$
Vậy x=4 thì thỏa mãn yêu cầu.