a. ĐKXĐ: $x\geq 1$

PT $\Leftrightarrow \frac{1}{2}\sqrt{x-1}-\frac{3}{2}.\sqrt{9}.\sqrt{x-1}+24.\sqrt{\frac{1}{64}}.\sqrt{x-1}=-17$

$\Leftrightarrow \frac{1}{2}\sqrt{x-1}-\frac{9}{2}\sqrt{x-1}+3\sqrt{x-1}=-17$

$\Leftrightarrow -\sqrt{x-1}=-17$

$\Leftrightarrow \sqrt{x-1}=17$

$\Leftrightarrow x-1=289$

$\Leftrightarrow x=290$

b. ĐKXĐ: $x\geq \frac{1}{2}$

PT $\Leftrightarrow \sqrt{9}.\sqrt{2x-1}-0,5\sqrt{2x-1}+\frac{1}{2}.\sqrt{25}.\sqrt{2x-1}+\sqrt{49}.\sqrt{2x-1}=24$

$\Leftrightarrow 3\sqrt{2x-1}-0,5\sqrt{2x-1}+2,5\sqrt{2x-1}+7\sqrt{2x-1}=24$
$\Leftrightarrow 12\sqrt{2x-1}=24$

$\Leftrihgtarrow \sqrt{2x-1}=2$

$\Leftrightarrow x=2,5$ (tm)

c. ĐKXĐ: $x\geq 2$

PT $\Leftrightarrow \sqrt{36}.\sqrt{x-2}-15\sqrt{\frac{1}{25}}\sqrt{x-2}=4(5+\sqrt{x-2})$

$\Leftrightarrow 6\sqrt{x-2}-3\sqrt{x-2}=20+4\sqrt{x-2}$

$\Leftrightarrow \sqrt{x-2}=-20< 0$ (vô lý)

Vậy pt vô nghiệm

\(\sqrt{36x-72}-15\sqrt{\dfrac{x-2}{25}}=4\left(5+\sqrt{x-2}\right)\) \(\left(x\text{≥}2\right)\)

⇔ \(\sqrt{36\left(x-2\right)}-15.\dfrac{\sqrt{x-2}}{5}=20+4\sqrt{x-2}\)

⇔ \(6\sqrt{x-2}-3\sqrt{x-2}-4\sqrt{x-2}=20\)

⇔ \(-\sqrt{x-2}=20\) ( vô lý )

KL : Phương trình vô nghiệm .

Đặt \(\sqrt{x-2}=\:a\)(a >= 0)

Ta có 6a - 3a = 4(5 + a)

<=> a = - 20 (không thỏa điều kiện)

Vậy phương trình vô nghiệm

bạn giải rõ hơn chút nữa được không? Mình cám ơn nhiều

Lời giải:

a) ĐK: $x\geq 2$

PT $\Leftrightarrow \sqrt{36(x-2)}-15\sqrt{\frac{1}{25}.(x-2)}=4(5+\sqrt{x-2})$

$\Leftrightarrow 6\sqrt{x-2}-3\sqrt{x-2}=20+4\sqrt{x-2}$

$\Leftrightarrow \sqrt{x-2}=-20< 0$ (vô lý)

Vậy pt vô nghiệm.

b) ĐK: $x\geq \frac{1}{2}$

PT $\Leftrightarrow \sqrt{2x-2\sqrt{2x-1}}=2$

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

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

$\Leftrightarrow |\sqrt{2x-1}-1|=2$

$\Leftrightarrow \sqrt{2x-1}-1=\pm 2$

$\Leftrightarrow \sqrt{2x-1}=3$ (chọn) hoặc $\sqrt{2x-1}=-1$

$\Rightarrow x=5$ (thỏa mãn)

3.

PT \(\left\{\begin{matrix} x+2\geq 0\\ 3x^2=(x+2)^2\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\geq -2\\ 2x^2-4x-4=0\end{matrix}\right.\Rightarrow x=1\pm \sqrt{3}\)

Lời giải:

a) ĐK: $x\geq 2$

PT $\Leftrightarrow \sqrt{36(x-2)}-15\sqrt{\frac{1}{25}.(x-2)}=4(5+\sqrt{x-2})$

$\Leftrightarrow 6\sqrt{x-2}-3\sqrt{x-2}=20+4\sqrt{x-2}$

$\Leftrightarrow \sqrt{x-2}=-20< 0$ (vô lý)

Vậy pt vô nghiệm.

b) ĐK: $x\geq \frac{1}{2}$

PT $\Leftrightarrow \sqrt{2x-2\sqrt{2x-1}}=2$

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

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

$\Leftrightarrow |\sqrt{2x-1}-1|=2$

$\Leftrightarrow \sqrt{2x-1}-1=\pm 2$

$\Leftrightarrow \sqrt{2x-1}=3$ (chọn) hoặc $\sqrt{2x-1}=-1$

$\Rightarrow x=5$ (thỏa mãn)

3.

PT \(\left\{\begin{matrix} x+2\geq 0\\ 3x^2=(x+2)^2\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\geq -2\\ 2x^2-4x-4=0\end{matrix}\right.\Rightarrow x=1\pm \sqrt{3}\)

a) ĐKXĐ : \(3\le x\le7\)

Ta có \(A=1.\sqrt{x-3}+1.\sqrt{7-x}\)

\(\le\sqrt{\left(1+1\right)\left(x-3+7-x\right)}=\sqrt{8}\)(BĐT Bunyacovski)

Dấu "=" xảy ra <=> \(\dfrac{1}{\sqrt{x-3}}=\dfrac{1}{\sqrt{7-x}}\Leftrightarrow x=5\)

Max và min chứ có ngu đến mức k bt lm cái đó đâu

1. ĐKXĐ:...

\(8-2x-\dfrac{2}{x}-2\sqrt{2-x^2}-2\sqrt{2-\dfrac{1}{x^2}}=0\)

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

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

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

\(\Leftrightarrow x=1\)

2.

ĐKXĐ:...

Ta có:

\(VT=x\sqrt{x}+1.\sqrt{12-x}\le\sqrt{\left(x^2+1\right)\left(x+12-x\right)}=2\sqrt{3\left(x^2+1\right)}\)

Dấu "=" xảy ra khi và chỉ khi: \(x\sqrt{12-x}=\sqrt{x}\)

\(\Leftrightarrow x^3-12x^2+x=0\Rightarrow\left[{}\begin{matrix}x=0\\x=6-\sqrt{35}\\x=6+\sqrt{35}\end{matrix}\right.\)

ai giúp với ạ :<

2: Ta có: \(A=\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\right):\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-1}\right)\)

\(=\dfrac{\sqrt{a}-\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\dfrac{a-1-a+4}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}\)

\(=\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}{3}\)

\(=\dfrac{\sqrt{a}-2}{3\sqrt{a}}\)