Đề bài \(ĐK\left(x\ge-\frac{3}{2}\right)\)

\(=>\left(x-3\right)^2+\left(\sqrt{2x+3}-3\right)^2=0\)

mà \(\left(x-3\right)^2+\left(\sqrt{2x+3}-3\right)^2\ge0\)

dấu = xảy ra khi x=3 (chọn )

zậy...

:V cách khác

Ta có:

\(x^2-4x+21=6\sqrt{2x+3}\left(x\ge-\frac{3}{2}\right)\)

\(\Leftrightarrow x^2-4x+21-18=6\left(\sqrt{2x+3}-3\right)\)

\(\Leftrightarrow x^2-4x+3=6\cdot\frac{2x-6}{\sqrt{2x+3}+3}\)

\(\Leftrightarrow\left(x-3\right)\left(x-1\right)-\frac{12\left(x-3\right)}{\sqrt{2x+3}+3}=0\)

\(\Leftrightarrow\left(x-3\right)\left[x-1-\frac{12}{\sqrt{2x+3}+3}\right]=0\)

:V

a) 3x + 18 = 0

<=>  3*(x+6)=0

<=> x+6=0

<=> x=-6

Vậy S={-6}

6x-7=3x+2

<=> 6x - 3x= 2+7

<=> 3x=9

<=> x=3 

Vậy S={ 3}

c) mk ko hỉu rõ đề

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

ta có \(y^2-2y+3=\left(y-1\right)^2+2\ge2\)(1)

   \(x^2+2x+4=\left(x+1\right)^2+3\ge3\)

==> \(\frac{6}{\left(x+1\right)^2+3}\le\frac{6}{3}=\)(2)

từ (1) và (2) thì để dấu = xảy ra khi 2 vế cùng =2

khi đó y-1=0 <=> y=1

     x+1=0  <=> x=-1

ĐK : \(x\ge\dfrac{-5}{2}\) PT tương đương

\(\Leftrightarrow\sqrt{2x+5}-3+\sqrt{x^2+5}-3=0\)

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

đến đây thì ez rồi

ĐKXĐ: \(x\ge1;x\le-3;x=-1\)

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

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+1}=0\left(1\right)\\\sqrt{2\left(x+3\right)}-\sqrt{x-1}=2\sqrt{x+1}\left(2\right)\end{matrix}\right.\)

\(\left(1\right)\Leftrightarrow x+1=0\Rightarrow x=-1\)

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

\(\Leftrightarrow2x+6=x-1+4\sqrt{\left(x-1\right)\left(x+1\right)}+4x+4\)

\(\Leftrightarrow4\sqrt{x^2-1}=3-3x\) \(\Leftrightarrow\left\{{}\begin{matrix}3-3x\ge0\\16\left(x^2-1\right)=\left(3-3x\right)^2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\le1\\7x^2+18x-25=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{-25}{7}\end{matrix}\right.\)

Vậy pt có 3 nghiệm: \(x=-1;1;\dfrac{-25}{7}\)