d) 3x^2 + 12x - 2 = 0 (1)
Delta = 12^2 - 4.3.(-2) = 168
Delta > 0 nên (1) có 2 nghiệm phân biệt:
x_1 = (-12 + sqrt(delta))/(2.3)
= (-12 + sqrt(168))/6
= (-6 + sqrt(42))/3
x_2 = (-12 - sqrt(delta))/(2.3)
= (-12 - sqrt(168))/6
= (-6 - sqrt(42))/3
e) x^2 + 2sqrt(5)x - 1 = 0 (2)
Delta = (2sqrt(5))^2 - 4.1.(-1) = 24
Delta > 0 nên pt (2) có 2 nghiệm phân biệt:
x_1 = (-2sqrt(5) + sqrt(delta))/(2.1)
= (-2sqrt(5) + sqrt(24))/2
= sqrt(6) - sqrt(5)
x_2 = (-2sqrt(5) - sqrt(delta))/(2.1)
= (-2sqrt(5) - sqrt(24))/2
= -sqrt(6) - sqrt(5)
\(d,\Delta'=6^2-\left(-2\right)\cdot3=42>0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-6-\sqrt{42}}{3}\\x=\dfrac{-6+\sqrt{42}}{3}\end{matrix}\right.\)
\(e,\Delta'=\left(\sqrt{5}\right)^2-\left(-1\right)\cdot1=6\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-\sqrt{5}-\sqrt{6}}{1}=-\sqrt{5}-\sqrt{6}\\x=\dfrac{-\sqrt{5}+\sqrt{6}}{1}=-\sqrt{5}+\sqrt{6}\end{matrix}\right.\)
