giải chi tiết hộ nhé.

Question

1/$\frac{x^{2}}{\sqrt{3x-2}}-\sqrt{3x-2}>1-x$

2/$4(x+1)^{2}<(2x+10)(1-\sqrt{3x+2})$

3/$\frac{2x}{\sqrt{2x+9}}<\sqrt{1+2x}-1$

4/$\sqrt{x+\frac{1}{x^{2}}}+ \sqrt{x-\frac{1}{x^{2}}}>\frac{2}{x} $

score 3 · Answer 1

1: ĐK $x>\dfrac{2}{3}$

BPT $\Leftrightarrow (x^2-3x+2)>(1-x)\sqrt{3x-2}$

$\Leftrightarrow (x-1)(x-2) +(x-1)\sqrt{3x-2}>0$

$(x-1) [ x-2 +\sqrt{3x-2} ] >0 \ (*)$

TH1: $x>1 \Rightarrow \sqrt{3x-2} -2+x >0 \ (*)$ đúng

TH2: $\dfrac{2}{3} <x <1 \Rightarrow \sqrt{3x-2} -2+x<0 \ (*)$ đúng

KL: $\left [ \begin{matrix} x>1 \\ \dfrac{2}{3} <x <1 \end{matrix} \right.$

1 Đáp án