Question

Answer 1

\(A=\sqrt{m^2+2m+1}+\sqrt{m^2-2m+1}\\ A=\sqrt{\left(m+1\right)^2}+\sqrt{\left(m-1\right)^2}\\ A=\left|m+1\right|+\left|m-1\right|=\left|m+1\right|+\left|1-m\right|\ge\left|m+1+1-m\right|=\left|2\right|=2\)

Dấu "=" \(\Leftrightarrow m+1=1-m\Leftrightarrow m=0\)

\(B=\sqrt{4a^2-4a+1}+\sqrt{4a^2-12a+9}\\ B=\sqrt{\left(2a-1\right)^2}+\sqrt{\left(2a-3\right)^2}\\ A=\left|2a-1\right|+\left|2a-3\right|=\left|2a-1\right|+\left|3-2a\right|\ge\left|2a-1+3-2a\right|=\left|2\right|=2\)

Dấu "=" \(\Leftrightarrow2a-1=3-2a\Leftrightarrow a=1\)

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