Question

cho -1<x<1 CMR: 5-3x/căn1-x^2 >=4

Answer 1

Đặt \(\sqrt{1+x}=a;\sqrt{1-x}=b\), \(a,b>0\)

Áp dụng BĐT AG-GM:

\(\Rightarrow A=\dfrac{a^2+4b^2}{ab}\ge\dfrac{2\sqrt{a^2\cdot4b^2}}{ab}=4\)

Dấu "=" \(\Leftrightarrow1+x=4\left(1-x\right)\Leftrightarrow x=\dfrac{3}{5}\left(N\right)\)

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