Question

Ai giải giúp em câu này với: giải pt:

(x - \(\sqrt{2}\))+3(x²-2) = 0

 

Answer 1

\(\left(x-\sqrt{2}\right)+3.\left(x^2-2\right)=0\)

\(\Leftrightarrow\left(x-\sqrt{2}\right)+3.\left(x^2-\sqrt{2}^2\right)=0\)

\(\Leftrightarrow\left(x-\sqrt{2}\right)+3.\left(x-\sqrt{2}\right).\left(x+\sqrt{2}\right)=0\)

\(\Leftrightarrow\left(x-\sqrt{2}\right).\left[1+3.\left(x+\sqrt{2}\right)\right]=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-\sqrt{2}=0\\1+3.\left(x+\sqrt{2}\right)=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\sqrt{2}\\x+\sqrt{2}=-\frac{1}{3}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\sqrt{2}\\x=-\frac{1}{3}-\sqrt{2}\end{cases}}}}\)

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