Question

Giải các phương trình sau:

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

2. \(\sqrt{x^2-2x+1}\) = x² -1

3. \(\sqrt{4x^2-4x+1}\) = x-1

4.\(\sqrt{x^4-2x^2+1}\) = x-1

5.\(\sqrt{x^2+x+\dfrac{1}{4}}\) =x

6.\(\sqrt{x^4-8x^2+16}\) =2-x

7. \(\sqrt{9x^2+6x+1}=\sqrt{11-6\sqrt{2}}\)

Answer 1

2: \(\Leftrightarrow\left|x-1\right|=x^2-1\)

\(\Leftrightarrow\left(x-1\right)^2=\left(x-1\right)^2\left(x+1\right)^2\)

\(\Leftrightarrow\left(x-1\right)^2\cdot x\cdot\left(x+2\right)=0\)

hay \(x\in\left\{1;0;-2\right\}\)

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

hay \(x\in\varnothing\)