Toán Lớp 7: lẹ1
Tìm giá trị nhỏ nhất của A:
A=|x-2020|+|x-2021|+|x-2022|
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Toán Lớp 7: lẹ1
Tìm giá trị nhỏ nhất của A:
A=|x-2020|+|x-2021|+|x-2022|
Comments ( 1 )
Answer
A = |x – 2020| + |x – 2021| + |x – 2022|
A = |x – 2020| + |x – 2022| + |x – 2021|
A = |x – 2020| + |- (x – 2022)| + |x – 2021|
A = |x – 2020| + |2022 – x| + |x – 2021|
A = (|x – 2020| + |2022 – x|) + |x – 2021|
Áp dụng BĐT |a| + |b| $\geqslant$ |a + b| ta có:
=> |x – 2020| + |2022 – x| $\geqslant$ |(x – 2020) + (2022 – x)|
=> |x – 2020| + |2022 – x| $\geqslant$ |x – 2020 + 2022 – x|
=> |x – 2020| + |2022 – x| $\geqslant$ |(x – x) + (2022 – 2020)|
=> |x – 2020| + |2022 – x| $\geqslant$ |2|
=> |x – 2020| + |2022 – x| $\geqslant$ 2
Vì |x – 2021| $\geqslant$ 0 AA x
Dấu $”=”$ xảy ra
<=> x – 2021 = 0
<=> x = 0 + 2021
<=> x = 2021
Vậy $A_{min}$ = 2 khi x = 2021