Question

Tìm GTNN của:

\(A=\sqrt{x-2\sqrt{x-3}}\)

\(B=\sqrt{\left(x-2011\right)^2}+\sqrt{\left(x-1\right)^2}\)

Answer 1

A = \(\sqrt{\left(x-3\right)-2\sqrt{x-3}+1+2}\)

= \(\sqrt{\left(\sqrt{x-3}-1\right)^2+2}\)\(\ge\)\(\sqrt{0+2}\)=\(\sqrt{2}\)

''='' <=> x = 4

=> Min A = \(\sqrt{2}\)và x = 4

B = |x-2011| + |x-1|

TH1: x \(\le\)1

=> B = 2012 - 2x \(\ge\)2010   ''='' <=> x = 1

TH2: 1\(\le\)x\(\le\)2011

=> B = x - 1 + 2011 - x = 2010 với mọi x t/m đkiện

TH3: x \(\ge\)2011

=> B = 2x - 2012 \(\ge\)2010 ''='' <=> x = 2011

Vậy Min B = 2010 <=> 1\(\le\)x\(\le\)2011