Question

Tìm MinA: \(\sqrt{x-2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}}\)

Help meee pls :<<

Answer 1

\(A=\sqrt{x-2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}}\)

\(=\sqrt{x-1-2\sqrt{x-1}+1}+\sqrt{x-1+2\sqrt{x-1}+1}\)

\(=\sqrt{\left(\sqrt{x-1}-1\right)^2}+\sqrt{\left(\sqrt{x-1}+1\right)^2}\)

\(=\left|\sqrt{x-1}-1\right|+\left|\sqrt{x-1}+1\right|\)

\(=\left|1-\sqrt{x-1}\right|+\left|\sqrt{x-1}+1\right|\)

\(\ge\left|1-\sqrt{x-1}+\sqrt{x-1}+1\right|=2\)

Dấu "=" xảy ra \(\Leftrightarrow\left(1-\sqrt{x-1}\right)\left(\sqrt{x-1}+1\right)\ge0\Leftrightarrow0\le x\le2\)

Vậy \(A_{min}=2\) tại \(0\le x\le2\)

Answer 2

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Answer 3

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Answer 4

vay a =2 0<x<2 nha bn

Answer 5

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Answer 6

A=√X-2√X-1+ √X