Question

[Chan]

a) \(\sqrt{36x-72}-15\sqrt{\frac{x-2}{25}}=4\left(5+\sqrt{x-2}\right)\)

b) \(\sqrt{x-\sqrt{2x-1}}=\sqrt{2}\)

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

Answer 1

[Cao Ngọc Diệp]

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

Answer 2

[Akai Haruma]

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