Question

[na kie]

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 chứng minh căn 2016 - 2* căn  2017 + căn 2018 < 0

Answer 1

[Linh Phong]

cần CM: \(\sqrt{2018}+\sqrt{2016}< \)\(2\sqrt{2017}\)

<=> \(2018+2016+2\sqrt{2018\cdot2016}< \)\(4\cdot17\)

<=>\(\sqrt{2018\cdot2016}< \)\(17\)

<=>\(\sqrt{2017^2-1}\)\(< \sqrt{2017^2}\) (BĐT luôn đúng)

Do đó \(\sqrt{2016}-2\sqrt{2017}+\sqrt{2018}< 0\)