Question

Giải phương trình:

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

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

3. \(\sqrt{x^2-\dfrac{7}{x^2}}+\sqrt{x-\dfrac{7}{x^2}}=x\)

4. \(\sqrt[3]{7x+1}+\sqrt[3]{x^2-x+8}+\sqrt[3]{x^2-8x-1}=2\)

Answer 1

4) Ta có pt \(\Leftrightarrow\dfrac{7x+1+x^2-8x-1}{\sqrt[3]{\left(7x+1\right)^2}-\sqrt[3]{\left(7x+1\right)\left(x^2-8x-1\right)}+\sqrt[3]{\left(x^2-8x+1\right)^2}}+\dfrac{x^2-x+8-8}{\sqrt[3]{\left(x^2-x+8\right)^2}+2\sqrt[3]{x^2-x+8}+4}=0\)

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

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

Answer 2

2) Ta có pt \(\Leftrightarrow\sqrt{x\left(x+1\right)}-\sqrt{x-1}=\sqrt{x}\Leftrightarrow x\left(x+1\right)=\left(\sqrt{x}+\sqrt{x-1}\right)^2\)

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

\(\Leftrightarrow x^2-x-1=2.\dfrac{x^2-x-1}{\sqrt{x^2-x}+1}\Leftrightarrow\left(x^2-x-1\right)\left(1-\dfrac{2}{\sqrt{x^2-x}+1}\right)=0\)...đến đấy chắc tự làm tiếp được

Answer 3

Câu 4 có cả nghiệm là x = -1 nữa

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