Câu hỏi:
22/07/2024 169
Với x = 2023 hãy tính giá trị của biểu thức: \[{\rm{B}} = \frac{1}{{{\rm{x}} - 23}} - \frac{1}{{{\rm{x}} - 3}}\].
A. \[{\rm{B}} = \frac{1}{{2\,\,020}}\]
B. \[{\rm{B}} = \frac{1}{{202\,\,000}}\]
C. \[{\rm{B}} = \frac{1}{{200\,\,200}}\]
D. \[{\rm{B}} = \frac{1}{{20\,\,200}}\]
Trả lời:
Lời giải
Đáp án đúng là: B
\[{\rm{B}} = \frac{1}{{{\rm{x}} - 23}} - \frac{1}{{{\rm{x}} - 3}} = \frac{{x - 3}}{{\left( {x - 23} \right)\left( {x - 3} \right)}} - \frac{{x - 23}}{{\left( {x - 23} \right)\left( {x - 3} \right)}}\]
\[ = \frac{{\left( {x - 3} \right) - \left( {x - 23} \right)}}{{\left( {x - 23} \right)\left( {x - 3} \right)}} = \frac{{x - 3 - x + 23}}{{\left( {x - 23} \right)\left( {x - 3} \right)}} = \frac{{20}}{{\left( {x - 23} \right)\left( {x - 3} \right)}}\]
Với x = 2023, ta có:
\[{\rm{B}} = \frac{{20}}{{\left( {2023 - 23} \right)\left( {2023 - 3} \right)}} = \frac{{20}}{{2000\,.\,2020}}\]
\[ = \frac{{20}}{{20\,.\,\,100\,.\,2020}} = \frac{1}{{100\,.\,2020}} = \frac{1}{{202\,\,000}}\].
Lời giải
Đáp án đúng là: B
\[{\rm{B}} = \frac{1}{{{\rm{x}} - 23}} - \frac{1}{{{\rm{x}} - 3}} = \frac{{x - 3}}{{\left( {x - 23} \right)\left( {x - 3} \right)}} - \frac{{x - 23}}{{\left( {x - 23} \right)\left( {x - 3} \right)}}\]
\[ = \frac{{\left( {x - 3} \right) - \left( {x - 23} \right)}}{{\left( {x - 23} \right)\left( {x - 3} \right)}} = \frac{{x - 3 - x + 23}}{{\left( {x - 23} \right)\left( {x - 3} \right)}} = \frac{{20}}{{\left( {x - 23} \right)\left( {x - 3} \right)}}\]
Với x = 2023, ta có:
\[{\rm{B}} = \frac{{20}}{{\left( {2023 - 23} \right)\left( {2023 - 3} \right)}} = \frac{{20}}{{2000\,.\,2020}}\]
\[ = \frac{{20}}{{20\,.\,\,100\,.\,2020}} = \frac{1}{{100\,.\,2020}} = \frac{1}{{202\,\,000}}\].