A = $\frac{√ x}{√ x + 3}$ Tính A biết x = $\frac{2 – √ 3}{2}$ 03/07/2021 Bởi Bella A = $\frac{√ x}{√ x + 3}$ Tính A biết x = $\frac{2 – √ 3}{2}$
Đáp án: $\begin{array}{l}x = \frac{{2 – \sqrt 3 }}{2} = \frac{{4 – 2\sqrt 3 }}{4} = \frac{{{{\left( {\sqrt 3 – 1} \right)}^2}}}{{{2^2}}} = {\left( {\frac{{\sqrt 3 – 1}}{2}} \right)^2}\\ \Rightarrow \sqrt x = \frac{{\sqrt 3 – 1}}{2}\\ \Rightarrow A = \frac{{\sqrt x }}{{\sqrt x + 3}} = \frac{{\frac{{\sqrt 3 – 1}}{2}}}{{\frac{{\sqrt 3 – 1}}{2} + 3}} = \frac{{\sqrt 3 – 1}}{{\sqrt 3 – 1 + 6}}\\ = \frac{{\sqrt 3 – 1}}{{\sqrt 3 + 5}} = \frac{{\left( {\sqrt 3 – 1} \right)\left( {\sqrt 3 – 5} \right)}}{{3 – 25}}\\ = \frac{{3 – 6\sqrt 3 + 5}}{{ – 22}} = \frac{{6\sqrt 3 – 8}}{{22}} = \frac{{3\sqrt 3 – 4}}{{11}}\end{array}$ Bình luận
Đáp án:
$\begin{array}{l}
x = \frac{{2 – \sqrt 3 }}{2} = \frac{{4 – 2\sqrt 3 }}{4} = \frac{{{{\left( {\sqrt 3 – 1} \right)}^2}}}{{{2^2}}} = {\left( {\frac{{\sqrt 3 – 1}}{2}} \right)^2}\\
\Rightarrow \sqrt x = \frac{{\sqrt 3 – 1}}{2}\\
\Rightarrow A = \frac{{\sqrt x }}{{\sqrt x + 3}} = \frac{{\frac{{\sqrt 3 – 1}}{2}}}{{\frac{{\sqrt 3 – 1}}{2} + 3}} = \frac{{\sqrt 3 – 1}}{{\sqrt 3 – 1 + 6}}\\
= \frac{{\sqrt 3 – 1}}{{\sqrt 3 + 5}} = \frac{{\left( {\sqrt 3 – 1} \right)\left( {\sqrt 3 – 5} \right)}}{{3 – 25}}\\
= \frac{{3 – 6\sqrt 3 + 5}}{{ – 22}} = \frac{{6\sqrt 3 – 8}}{{22}} = \frac{{3\sqrt 3 – 4}}{{11}}
\end{array}$