Question

So sánh

a) A= \(\sqrt{3}-\sqrt{2}\) và B = \(\sqrt{6}-\sqrt{5}\)

b) A= \(\sqrt{2018}+\sqrt{2014}+\sqrt{2010}\)

B= \(\sqrt{2011}+\sqrt{2015}+\sqrt{2016}\)

Answer 1

a) A = \(\sqrt{3}-\sqrt{2}\) và B = \(\sqrt{6}-\sqrt{5}\)

Giả sử : \(\sqrt{3}-\sqrt{2}\le\sqrt{6}-\sqrt{5}\)

⇔ \(\left(\sqrt{3}-\sqrt{2}\right)^2\le\left(\sqrt{6}-\sqrt{5}\right)^2\)

⇔ 5 - \(2\sqrt{6}\) ≤ 11 - \(2\sqrt{30}\)

⇔ \(2\sqrt{30}-2\sqrt{6}\) ≤ 6

⇔\(\left(2\sqrt{30}-2\sqrt{6}\right)^2\le6^2\)

⇔ 36, 66 ≤ 36 (sai)

Vậy \(\sqrt{3}-\sqrt{2}>\sqrt{6}-\sqrt{5}\)

Answer 2

a) ta có : \(8+2\sqrt{15}>8+2\sqrt{12}\Leftrightarrow\left(\sqrt{3}+\sqrt{5}\right)^2>\left(\sqrt{6}+\sqrt{2}\right)^2\)

\(\Leftrightarrow\sqrt{3}+\sqrt{5}>\sqrt{6}+\sqrt{2}\Leftrightarrow\sqrt{3}-\sqrt{2}>\sqrt{6}-\sqrt{5}\)

câu b tương tự nha

Answer 3

Mysterious Person DƯƠNG PHAN KHÁNH DƯƠNG Khánh Như Trương Ngọc giúp mk nhá

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