Question

cho -1<x<1 CMR: 5-3x/1-x^2 >=4

Answer 1

\(\dfrac{5-3x}{1-x^2}=\dfrac{10-6x}{2\left(1-x^2\right)}=\dfrac{9\left(1-x^2\right)+9x^2-6x+1}{2\left(1-x^2\right)}=\dfrac{9}{2}+\dfrac{\left(3x-1\right)^2}{2\left(1-x^2\right)}\ge\dfrac{9}{2}\)

Dấu "=" xảy ra khi \(x=\dfrac{1}{3}\)

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