\(a.x^2-6x-2=0.\\ \Delta'=3^2+2=11>0.\Rightarrow\left\{{}\begin{matrix}x_1=3+\sqrt{11}.\\x_2=3-\sqrt{11}.\end{matrix}\right.\)
\(b.3x^2+5x-1=0.\\ \Delta=5^2-4.3.\left(-1\right)=37>0.\Rightarrow\left\{{}\begin{matrix}x_1=\dfrac{-5+\sqrt{37}}{6}.\\x_2=\dfrac{-5-\sqrt{37}}{6}.\end{matrix}\right.\)
\(c.-3x^2+14x-10=0.\\ \Delta'=7^2+3.\left(-10\right)=19>0.\Rightarrow\left\{{}\begin{matrix}x_1=\dfrac{7+\sqrt{19}}{3}.\\x_2=\dfrac{7-\sqrt{19}}{3}.\end{matrix}\right.\)
Bài 3:
a: \(\Delta=\left(1-2\sqrt{2}\right)^2+4\cdot2\cdot\sqrt{2}=9-4\sqrt{2}+8\sqrt{2}=9+4\sqrt{2}>0\)
Do đó: Phương trình có hai nghiệm phân biệt là:
\(\left\{{}\begin{matrix}x_1=\dfrac{1-2\sqrt{2}-2\sqrt{2}-1}{4}=-\sqrt{2}\\x_2=\dfrac{1-2\sqrt{2}+2\sqrt{2}+1}{4}=\dfrac{1}{2}\end{matrix}\right.\)
b: \(\Leftrightarrow\sqrt{3}x^2+2x-1-2\sqrt{3}x-3=0\)
\(\Leftrightarrow\sqrt{3}x^2+\left(2-2\sqrt{3}\right)x-4=0\)
\(\Delta=\left(2-2\sqrt{3}\right)^2-4\cdot\sqrt{3}\cdot\left(-4\right)=16-8\sqrt{3}+16\sqrt{3}=16+8\sqrt{3}=\left(2\sqrt{3}+2\right)^2\)
Do đó: Phương trình có hai nghiệm phân biệt là:
\(\left\{{}\begin{matrix}x_1=\dfrac{-2+2\sqrt{3}-2\sqrt{3}-2}{2\sqrt{3}}=\dfrac{-4}{2\sqrt{3}}=\dfrac{-2\sqrt{3}}{3}\\x_2=\dfrac{-2+2\sqrt{3}+2\sqrt{3}+2}{2\sqrt{3}}=2\end{matrix}\right.\)
