Đặt: \(\sqrt{x+9}=v;\sqrt{x+6}=u\)

Ta có: \(v+5u=5+vu\)

\(\Leftrightarrow v+5u-5-uv=0\)

\(\Leftrightarrow-v\left(u-1\right)+5\left(u-1\right)\)

\(\Leftrightarrow\left(5-v\right)\left(u-1\right)\)

\(\left\{{}\begin{matrix}5-v=0\Leftrightarrow5=\sqrt{x+9}\Leftrightarrow x=16\left(N\right)\\u-1=0\Leftrightarrow\sqrt{x+6}=1\Leftrightarrow x=-5\left(L\right)\end{matrix}\right.\)          ĐKXĐ:\(x>=-6\)

\(S=\left\{16\right\}\)

Đặt:\(\sqrt{x+9}=v;\sqrt{x+6}=u\)

Ta có: \(v+5u=5+vu\Leftrightarrow-v\left(u-1\right)+5\left(u-1\right)\Leftrightarrow\left(5-v\right)\left(u-1\right)\)

\(\left\{{}\begin{matrix}5-v=0\Leftrightarrow5=\sqrt{x+9}\Leftrightarrow x=16\left(N\right)\\u-1=0\Leftrightarrow\sqrt{x+6}=1\Leftrightarrow x=-5\left(N\right)\end{matrix}\right.ĐKXĐ:x>=-6\)

\(S=\left\{16,-5\right\}\)

Câu trên mình quên -5>-6

=>\(x^2+9-12\sqrt{x^2-25}=13x+5-12\sqrt{x^2-25}\)

<=> \(x^2-13x+4=0\)

........

\(=>x^2+11-12\sqrt{x^2-25}=13x+25-12\sqrt{x^2-25}\)

\(< =>x^2-13x-14=0\)

\(< =>\left(x+1\right)\left(x-14\right)=0\)

..............

a.

\(3\sqrt{-x^2+x+6}\ge2\left(1-2x\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}-x^2+x+6\ge0\\1-2x< 0\end{matrix}\right.\\\left\{{}\begin{matrix}1-2x\ge0\\9\left(-x^2+x+6\right)\ge4\left(1-2x\right)^2\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}-2\le x\le3\\x>\dfrac{1}{2}\end{matrix}\right.\\\left\{{}\begin{matrix}x\le\dfrac{1}{2}\\25\left(x^2-x-2\right)\le0\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}< x\le3\\\left\{{}\begin{matrix}x\le\dfrac{1}{2}\\-1\le x\le2\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow-1\le x\le3\)

b.

ĐKXĐ: \(x\ge0\)

\(\Leftrightarrow\sqrt{2x^2+8x+5}-4\sqrt{x}+\sqrt{2x^2-4x+5}-2\sqrt{x}=0\)

\(\Leftrightarrow\dfrac{2x^2+8x+5-16x}{\sqrt{2x^2+8x+5}+4\sqrt{x}}+\dfrac{2x^2-4x+5-4x}{\sqrt{2x^2-4x+5}+2\sqrt{x}}=0\)

\(\Leftrightarrow\dfrac{2x^2-8x+5}{\sqrt{2x^2+8x+5}+4\sqrt{x}}+\dfrac{2x^2-8x+5}{\sqrt{2x^2-4x+5}+2\sqrt{x}}=0\)

\(\Leftrightarrow\left(2x^2-8x+5\right)\left(\dfrac{1}{\sqrt{2x^2+8x+5}+4\sqrt{x}}+\dfrac{1}{\sqrt{2x^2-4x+5}+2\sqrt{x}}\right)=0\)

\(\Leftrightarrow2x^2-8x+5=0\)

\(\Leftrightarrow x=\dfrac{4\pm\sqrt{6}}{2}\)

`sqrt{x^2-25}-6=3sqrt{x+5}-2sqrt{x-5}(x>=5)`

`<=>sqrt{(x-5)(x+5)}+2sqrt{x-5}=3sqrt{x+5}+6`

`<=>sqrt{x-5}(sqrt{x+5}+2)=3(sqrt{x+5}+2)`

`<=>(sqrt{x+5}+2)(sqrt{x-5}-3)=0`

Vì `sqrt{x+5}+2>0`

`<=>sqrt{x-5}-3=0`

`<=>sqrt{x-5}=3`

`<=>x-5=9<=>x=14(tm)`

Vậy `x=14`

\(\sqrt{x^2-25}-6=3\sqrt{x+5}-2\sqrt{x-5}\\ \Leftrightarrow\sqrt{\left(x-5\right)\left(x+5\right)}-6-3\sqrt{x+5}+2\sqrt{x-5}=0\\ \Leftrightarrow\left(2\sqrt{x-5}+\sqrt{\left(x-5\right)\left(x+5\right)}\right)-\left(3\sqrt{x+5}+6\right)=0\Leftrightarrow\sqrt{x-5}\left(2+\sqrt{x+5}\right)-3\left(2+\sqrt{x+5}\right)=0\\ \Leftrightarrow\left(\sqrt{x-5}-3\right)\left(2+\sqrt{x-5}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}\sqrt{x-5}=3\\\sqrt{x-5}=-2\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x-5=9\\x\in\varnothing\end{matrix}\right.\Leftrightarrow x=14\)

\(ĐK:x\le1\)

Đặt \(\sqrt{1-x}=t\ge0\Leftrightarrow x=1-t^2\)

\(PT\Leftrightarrow6t-\left(1-t^2\right)=5\sqrt{1-t}\\ \Leftrightarrow t^2-\left(1-t\right)+5t-5\sqrt{1-t}=0\\ \Leftrightarrow\left(t-\sqrt{1-t}\right)\left(t+\sqrt{1-t}+5\right)=0\\ \Leftrightarrow t-\sqrt{1-t}=0\left(t+\sqrt{1-t}+5>0\right)\\ \Leftrightarrow t=\sqrt{1-t}\\ \Leftrightarrow t^2=1-t\\ \Leftrightarrow t=\dfrac{\sqrt{5}-1}{2}\Leftrightarrow1-x=\dfrac{3-\sqrt{5}}{2}\\ \Leftrightarrow x=\dfrac{-1\pm\sqrt{5}}{2}\left(tm\right)\)

a: ĐKXĐ: \(\left\{{}\begin{matrix}x-3>=0\\5-x>=0\end{matrix}\right.\)

=>3<=x<=5

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

=>\(\sqrt{x-3}-1+\sqrt{5-x}-1=0\)

=>\(\dfrac{x-3-1}{\sqrt{x-3}+1}+\dfrac{5-x-1}{\sqrt{5-x}+1}=0\)

=>\(\left(x-4\right)\left(\dfrac{1}{\sqrt{x-3}+1}-\dfrac{1}{\sqrt{5-x}+1}\right)=0\)

=>x-4=0

=>x=4

\(PT\Leftrightarrow6\left(x+\sqrt{6x^2+6}\right)=-5x^2-2\sqrt{5}x-1\)

\(\Leftrightarrow6\left(x+\sqrt{6x^2+6}\right)=-\left(\sqrt{5}x+1\right)^2\)

\(\Rightarrow x+\sqrt{6x^2+6}\le0\)

rồi sao nữa

cái này nhân trên tử một lượng giống hệt mẫu là ra hằng đẳng thức e nhé

ý bạn là sao ?

a. ĐKXĐ: \(x\ge3\)

\(\Leftrightarrow2x-5=x-3\)

\(\Leftrightarrow x=2\) (ktm)

Vậy pt vô nghiệm

b.

ĐKXĐ: \(x\in R\)

\(\Leftrightarrow x^2-x+6=x^2+3\)

\(\Leftrightarrow x=3\)

a. \(\sqrt[3]{1-2x}+3=0\left(ĐK:x\le\dfrac{1}{2}\right)\)

<=> \(\sqrt[3]{1-2x}=-3\)

<=> \(1-2x=\left(-3\right)^3\)

<=> \(1-2x=-27\)

<=> \(-2x=-28\)

<=> \(x=14\left(TM\right)\)