1 like tức thì nào

\(\left(\sqrt{2x+3}+2\right)\left(\sqrt{x+6}-\sqrt{x+1}\right)=5\)

\(ĐKXĐ:x\ge-1\).Nhận thấy \(\sqrt{x+6}-\sqrt{x+1}>0\)

\(\Leftrightarrow\left(\sqrt{2x+3}+2\right)\frac{\left(\sqrt{x+6}+\sqrt{x+1}\right)\left(\sqrt{x+6}-\sqrt{x+1}\right)}{\sqrt{x+6}-\sqrt{x+1}}=5\)

\(\Leftrightarrow\left(\sqrt{2x+3}+2\right)\frac{5}{\sqrt{x+6}-\sqrt{x+1}}=5\)

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

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

Th1:\(\sqrt{x+1}=2\Leftrightarrow x=3\left(thoaman\right)\)

Th2:\(\sqrt{x+1}-2\ne0\Leftrightarrow x\ne3\)

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

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

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

Tự lm tiếp nha

Nhận xét : \(\sqrt{\left(5-2\sqrt{6}\right)^x}.\sqrt{\left(5+2\sqrt{6}\right)^x}=1\)

Ta đặt \(\sqrt{\left(5-2\sqrt{6}\right)^x}=a\Rightarrow\sqrt{\left(5+2\sqrt{6}\right)^x}=\frac{1}{a}\)

Khi đó phương trình ban đầu trở thành :

\(a+\frac{1}{a}=10\Rightarrow a^2-10a+1=0\)

\(\Leftrightarrow\orbr{\begin{cases}a=5+2\sqrt{6}\\a=5-2\sqrt{6}\end{cases}}\)

+) Với \(a=5+2\sqrt{6}\Rightarrow\sqrt{\left(5-2\sqrt{6}\right)^x}=5+2\sqrt{6}\)

\(\Leftrightarrow\left(5-2\sqrt{6}\right)^x=\left(5+2\sqrt{6}\right)^2=\left(\frac{1}{5-2\sqrt{6}}\right)^2\)

\(\Leftrightarrow x=-2\)

+) Với \(a=5-2\sqrt{6}\Rightarrow\sqrt{\left(5-2\sqrt{6}\right)^x}=5-2\sqrt{6}\)

\(\Leftrightarrow\left(5-2\sqrt{6}\right)^x=\left(5-2\sqrt{6}\right)^2\)

\(\Leftrightarrow x=2\)

Vậy \(x\in\left\{-2,2\right\}\) thỏa mãn đề.

\(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-2\sqrt{2x-5}}=2\sqrt{2}\)

nhân 2 vế với căn 2 ta có 

\(\sqrt{2x+4+6\sqrt{2x-5}}+\sqrt{2x-4-2\sqrt{2x-5}}=4\)

<=>\(\sqrt{\left(\sqrt{2x-5}+3\right)^2}+\sqrt{\left(\sqrt{2x-5}-1\right)^2}=4\)

<=>\(\left|\sqrt{2x-5}+3\right|+\left|\sqrt{2x-5}-1\right|=4\)

đến đây bạn tự giải nốt nhé 

minh viet thieu nha :trên là VP ,VT=\(2\sqrt{2}\)

cam on ban nha

\(\left(5-2\sqrt{6}\right)^{\frac{x}{2}}+\left(5+2\sqrt{6}\right)^{\frac{x}{2}}=10\)

\(pt\Leftrightarrow\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^{2x}}+\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^{2x}}=10\)

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

\(\Leftrightarrow\frac{1}{\left(\sqrt{3}+\sqrt{2}\right)^x}+\left(\sqrt{3}+\sqrt{2}\right)^x=10\)

\(\Leftrightarrow\frac{1}{t}+t=10\left(t=\left(\sqrt{3}+\sqrt{2}\right)^x\right)\)

\(\Leftrightarrow t^2-10t+1=0\)\(\Leftrightarrow t=5\pm2\sqrt{6}\)

\(\Rightarrow5\pm2\sqrt{6}=\left(\sqrt{3}+\sqrt{2}\right)^x\)

\(\Leftrightarrow\left(\sqrt{3}+\sqrt{2}\right)^{\pm2}=\left(\sqrt{3}+\sqrt{2}\right)^x\)

\(\Rightarrow x=\pm2\). Vậy...

=>|x^2+2|=x^2+2x+5

=>x^2+2=x^2+2x+5(Do x^2+2>=2>0 với mọi x)

=>2x+5=2

=>2x=-3

=>x=-3/2

\(\sqrt{\left(x^2+2\right)^2}=x^2+2x+5\)

\(\Leftrightarrow\left|x^2+2\right|=x^2+2x+5\)  

Mà: \(x^2+2\ge2>0\forall x\)

\(\Leftrightarrow x^2+2=x^2+2x+5\)

\(\Leftrightarrow x^2-x^2+2x+5-2=0\)

\(\Leftrightarrow2x+3=0\)

\(\Leftrightarrow2x=-3\)

\(\Leftrightarrow x=-\dfrac{3}{2}\)

nhiều thế giải ko đổi đâu bạn

vậy trả lời câu a thôi

đkxđ : \(\frac{1}{2}\le x\le7\)

\(x^2-5x+3\sqrt{2x-1}=2\sqrt{14-2x}+5\)

\(\Leftrightarrow\left(x^2-5x\right)+3\left(\sqrt{2x-1}-3\right)=2\left(\sqrt{14-2x}-2\right)\)

\(\Leftrightarrow x\left(x-5\right)+\frac{3.\left(2x-10\right)}{\sqrt{2x-1}+3}+\frac{2.\left(2x-10\right)}{\sqrt{14-2x}+2}=0\)

\(\Leftrightarrow\left(x-5\right)\left(x+\frac{6}{\sqrt{2x-1}+3}+\frac{4}{\sqrt{14-2x}+2}\right)=0\)

\(\Leftrightarrow x=5\)

còn bài a,c lười đánh lắm

\(y=\frac{1}{x^2+\sqrt{x}}\left(nvb\int^{42}_{3^{2_{1\frac{12}{23}}}}\right)\)