Question

so sánh A và B biết A= \(\sqrt{2003}+\sqrt{2005}\) và B= \(2\sqrt{2004}\)

Answer 1

\(\left(\sqrt{2003}+\sqrt{2005}\right)^2=2003+2005+2\sqrt{2003.2005}=4008+2\sqrt{2003.2005}\)

\(\left(2\sqrt{2004}\right)^2=4.2004=2.2004+2.2004=4008+2.2004\)

TA có 2003.2005 = (2004 -1 )(2004 + 1 ) = 2004 ^2 - 1 <2004 ^2

=> 2003 . 2005 < 2004^2 =>\(\sqrt{2003.2005}

Answer 2

Ta có:2004²-1<2004⁴

=>2003.2005<2004²

=>2\(\sqrt{2003.2005}\)<2.2004

Do 2003+2005=2004+2004

=>2003+2\(\sqrt{2003.2005}\)+2005<2004+2.2004+2004

=>\(\left(\sqrt{2003}+\sqrt{2005}\right)^2

Answer 3

so sanh hai can bac hai so hoc sau

√(6+√6+√6) va 3