Toán Giải phương trình : 4-x/2018-2=3-x/2019-x/1011 19/07/2021 By Arianna Giải phương trình : 4-x/2018-2=3-x/2019-x/1011
Đáp án: `S={2022}.` Giải thích các bước giải: `(4-x)/2018-2=(3-x)/2019-x/1011` `(4-x)/2018-2+3 =(3-x)/2019-x/1011 +3 ` `<=>(4-x)/2018+1=(3-x)/2019+1 -x/1011 +2` `<=>(2022-x)/2018 = (2022-x)/2019 + (2022-x)/2011` `<=>(2022-x)/2018 – (2022-x)/2019 – (2022-x)/2011=0` `<=>(2022-x)(1/2018 -1/2019 -1/2011)=0` `<=>2022-x=0( vì 1/2018 -1/2019 -1/2011 \ne 0)` `<=>x=2022` Vậy phương trình có tập nghiệm `S={2022}.` Trả lời
Đáp án: $\begin{array}{l}\dfrac{4-x}{2018} – 2 = \dfrac{3-x}{2019} – \dfrac{x}{1011} \\ \Leftrightarrow \dfrac{4-x}{2018} – 2 + 3 = \dfrac{3-x}{2019} – \dfrac{x}{1011} + 3 \\ \Leftrightarrow \dfrac{4-x}{2018} + 1 = \dfrac{3-x}{2019} + 1 – \dfrac{x}{1011} + 2 \\ \Leftrightarrow \dfrac{4-x+2018}{2018} = \dfrac{3-x-2019}{2019} + \dfrac{-x+1011.2}{1011} \\ \Leftrightarrow \dfrac{2022-x}{2018} = \dfrac{2022-x}{2019} + \dfrac{2022-x}{1011} \\ \Leftrightarrow \dfrac{2022-x}{2018} – \dfrac{2022-x}{2019} – \dfrac{2022-x}{1011} = 0 \\ \Leftrightarrow ( 2022-x ) . ( \dfrac{1}{2018} – \dfrac{1}{2019} – \dfrac{1}{1011} ) = 0 \\ \Leftrightarrow 2022-x=0 \ \ (\text{Vì} \ \dfrac{1}{2018} – \dfrac{1}{2019} – \dfrac{1}{1011} \ne 0 )\\ \Leftrightarrow x=2022 \\ \text{Vậy} \ S=\{2022\} \end{array}$ Trả lời
Đáp án:
`S={2022}.`
Giải thích các bước giải:
`(4-x)/2018-2=(3-x)/2019-x/1011`
`(4-x)/2018-2+3 =(3-x)/2019-x/1011 +3 `
`<=>(4-x)/2018+1=(3-x)/2019+1 -x/1011 +2`
`<=>(2022-x)/2018 = (2022-x)/2019 + (2022-x)/2011`
`<=>(2022-x)/2018 – (2022-x)/2019 – (2022-x)/2011=0`
`<=>(2022-x)(1/2018 -1/2019 -1/2011)=0`
`<=>2022-x=0( vì 1/2018 -1/2019 -1/2011 \ne 0)`
`<=>x=2022`
Vậy phương trình có tập nghiệm `S={2022}.`
Đáp án:
$\begin{array}{l}\dfrac{4-x}{2018} – 2 = \dfrac{3-x}{2019} – \dfrac{x}{1011} \\ \Leftrightarrow \dfrac{4-x}{2018} – 2 + 3 = \dfrac{3-x}{2019} – \dfrac{x}{1011} + 3 \\ \Leftrightarrow \dfrac{4-x}{2018} + 1 = \dfrac{3-x}{2019} + 1 – \dfrac{x}{1011} + 2 \\ \Leftrightarrow \dfrac{4-x+2018}{2018} = \dfrac{3-x-2019}{2019} + \dfrac{-x+1011.2}{1011} \\ \Leftrightarrow \dfrac{2022-x}{2018} = \dfrac{2022-x}{2019} + \dfrac{2022-x}{1011} \\ \Leftrightarrow \dfrac{2022-x}{2018} – \dfrac{2022-x}{2019} – \dfrac{2022-x}{1011} = 0 \\ \Leftrightarrow ( 2022-x ) . ( \dfrac{1}{2018} – \dfrac{1}{2019} – \dfrac{1}{1011} ) = 0 \\ \Leftrightarrow 2022-x=0 \ \ (\text{Vì} \ \dfrac{1}{2018} – \dfrac{1}{2019} – \dfrac{1}{1011} \ne 0 )\\ \Leftrightarrow x=2022 \\ \text{Vậy} \ S=\{2022\} \end{array}$