Toán Lớp 9: \sqrt{x-2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}
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Toán Lớp 9: \sqrt{x-2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}
tìm gtnn
Comments ( 2 )
A=sqrt((x-1)-2sqrt(x-1)+1)+sqrt((x-1)+2sqrt(x-1)+1)
A=sqrt((sqrt(x-1)-1)^2)+sqrt((sqrt(x-1)+1)^2)
A=|sqrt(x-1)-1|+|sqrt(x-1)+1|
A=|1-sqrt(x-1)|+|sqrt(x-1)+1|
A>=|1-sqrt(x-1)+sqrt(x-1)+1|
A>=|1+1|
A>=|2|
A>=2
Xảy ra dấu “=” :
(sqrt(x-1)-1)(sqrt(x-1)+1)=0
<=>x-1-1=0
<=>x-2=0
<=>x=2
Vậy : A_min=2 khi x=2