Toán Lớp 7: |x-2013|+|x-2014|+|x-2020| Tìm GTNN -

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Toán Lớp 7: |x-2013|+|x-2014|+|x-2020| Tìm GTNN

Ayla Tháng Bảy 4, 2022 Toán học 2 Comments 0 views

Toán Lớp 7: |x-2013|+|x-2014|+|x-2020|
Tìm GTNN

Comments ( 2 )

annhocbichchaubich
4 Tháng Bảy, 2022 at 3:55 sáng

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$\text{ Đặt A = | x – 2013 | + | x – 2014 | + | x – 2020 | }$

$\text{ Ta có : }$

$\text{ | x – 2013 | + | x – 2020 | = | x – 2013 | + | 2020 – x | }$ $\ge$ | x – 2013 + 2020 – x | = | 7 | = 7

$\Rightarrow$ $\text{ A = | x – 2013 | + | x – 2014 | + | x – 2020 | $\ge$ 7 }$

$\text{ – Dấu “=” xảy ra }$ $\Leftrightarrow$ $\text{ x – 2014 = 0 }$

$\Leftrightarrow$ $\text{ x = 2014 }$

$\text{ Vậy Amin = 7 $\Leftrightarrow$ x = 2014 }$
behocgioitoan
4 Tháng Bảy, 2022 at 3:55 sáng

Reply

Đặt:

A=|x-2013|+|x-2014|+|x-2020|

A=|x-2013|+|x-2014|+|2020-x|

=>A>=|x-2013+0+2020-x|=7

Dấu $”$=$”$ xảy ra

<=>{(x-2013>=0),(x-2014=0),(x-2020<=0):}

<=>{(x>=2013),(x=2014(t//m)),(x<=2020):}

Vậy min A=7 khi x=2014

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