mình nghĩ sửa đề bài là  \(\frac{\sqrt{x^2-x+6}+7\sqrt{x}-\sqrt{6\left(x^2+5x-2\right)}}{x+3-\sqrt{2\left(x^2+10\right)}}\le0\) 

\(\frac{2x-5}{!x-3!}+1>0\Leftrightarrow\frac{2x-5+!x-3!}{!x-3}>0\)

do !x-3!>0 mọi x khác 3=> Bất phương trình tương đương

\(2x-5+!x-3!>0\Leftrightarrow!x-3!>5-2x\)

TH(1) x<3 <=>3-x>5-2x=> x>2

Kết luận(1) \(2< x< 3\)

TH(2) \(x\ge3\Leftrightarrow x-3>5-2x\Rightarrow3x>8\Rightarrow x>\frac{8}{3}\)

Kết luận(2) \(x\ge3\)

(1)và(2) nghiệm của Bpt là: x>2

Hung nguyen, Trần Thanh Phương, Sky SơnTùng, @tth_new, @Nguyễn Việt Lâm, @Akai Haruma, @No choice teen

help me, pleaseee

Cần gấp lắm ạ!

a/ \(\Leftrightarrow x^2+5x-2-2\sqrt[3]{x^2+5x-2}+4=0\)

Đặt \(\sqrt[3]{x^2+5x-2}=a\)

\(a^3-2a+4=0\)

\(\Leftrightarrow\left(a+2\right)\left(a^2-2a+2\right)=0\Rightarrow a=-2\)

\(\Rightarrow\sqrt[3]{x^2+5x-2}=-2\Rightarrow x^2+5x+6=0\Rightarrow...\)

b/ ĐKXĐ:...

\(\Leftrightarrow-3\left(-x^2+4x+10\right)-5\sqrt{-x^2+4x+10}+42=0\)

Đặt \(\sqrt{-x^2+4x+10}=a\ge0\)

\(-3a^2-5a+42=0\Rightarrow\left[{}\begin{matrix}a=3\\a=-\frac{14}{3}\left(l\right)\end{matrix}\right.\)

\(\Rightarrow\sqrt{x^2+4x+10}=3\Rightarrow x^2-4x-1=0\Rightarrow...\)

c/ ĐKXĐ: ...

\(\Leftrightarrow x^2+3x+3\sqrt{x^2+3x}-10=0\)

Đặt \(\sqrt{x^2+3x}=a\ge0\)

\(a^2+3a-10=0\Rightarrow\left[{}\begin{matrix}a=2\\a=-5\left(l\right)\end{matrix}\right.\)

\(\Rightarrow\sqrt{x^2+3x}=2\Rightarrow x^2+3x-4=0\)

d/ ĐKXĐ: \(-1\le x\le2\)

\(\Leftrightarrow\sqrt{3-x+x^2}=1+\sqrt{2+x-x^2}\)

\(\Leftrightarrow3-x+x^2=3+x-x^2+2\sqrt{2+x-x^2}\)

\(\Leftrightarrow2+x-x^2+\sqrt{2+x-x^2}-2=0\)

Đặt \(\sqrt{2+x-x^2}=a\ge0\)

\(a^2+a-2=0\Rightarrow\left[{}\begin{matrix}a=1\\a=-2\left(l\right)\end{matrix}\right.\)

\(\Rightarrow\sqrt{2+x-x^2}=1\Leftrightarrow x^2-x-1=0\)

e/ \(\Leftrightarrow\sqrt{x^2-3x+3}-1+\sqrt{x^2-3x+6}-2=0\)

\(\Leftrightarrow\frac{x^2-3x+2}{\sqrt{x^2-3x+3}+1}+\frac{x^2-3x+2}{\sqrt{x^2-3x+6}+2}=0\)

\(\Leftrightarrow\left(x^2-3x+2\right)\left(\frac{1}{\sqrt{x^2-3x+3}+1}+\frac{1}{\sqrt{x^2-3x+6}+2}\right)=0\)

\(\Leftrightarrow x^2-3x+2=0\)