Bất phương trình 10 pp đặt ẩn phụ

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leminhnghia1

2. $\dfrac{x}{x+1}-2\sqrt{\dfrac{x+1}{x}}>3$
3.$3\sqrt{x}+\dfrac{3}{2\sqrt{x}}<2x+\dfrac{1}{2x}-7$
4. $\sqrt{1+x}+\sqrt{1-x}$ \leq$2-\dfrac{x^2}{4}$


1,Đặt $\sqrt{\dfrac{x+1}{x}}=t \rightarrow \dfrac{x+1}{x}=\dfrac{1}{t^2} \ (t \not =0)$

Thay vào ta có: $\dfrac{1}{t^2}-2t>3$

$\iff -2t^3+1>3t^2$

$\iff (2t-1)(t+1)^2 <0$

$\iff t < \dfrac{1}{2}$

$\iff \dfrac{x+1}{x} < \dfrac{1}{4}$

$\iff \dfrac{3x+1}{x} <0$

$\iff -\dfrac{1}{3} <x<0$

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