ĐK: \(x\in R\)
Đặt \(\sqrt{3x^2-2x+15}=a,\sqrt{3x^2-2x+8}=b\left(a,b>0\right)\)
\(pt\Leftrightarrow a+b=a^2-b^2\)
\(\Leftrightarrow\left(a+b\right)\left(a-b-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=-b\left(l\right)\\a=b+1\end{matrix}\right.\)
\(a=b+1\)
\(\Leftrightarrow\sqrt{3x^2-2x+15}=\sqrt{3x^2-2x+8}+1\)
\(\Leftrightarrow3x^2-2x+15=3x^2-2x+8+1+2\sqrt{3x^2-2x+8}\)
\(\Leftrightarrow\sqrt{3x^2-2x+8}=3\)
\(\Leftrightarrow3x^2-2x+8=9\)
\(\Leftrightarrow3x^2-2x-1=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{3}\end{matrix}\right.\)
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