a/ \(\Delta=\left(3\sqrt{3}\right)^2-4.4\left(-6\right)=123\)
\(\Rightarrow\left\{{}\begin{matrix}x_1=\frac{3\sqrt{3}+\sqrt{123}}{8}\\x_2=\frac{3\sqrt{3}-\sqrt{123}}{8}\end{matrix}\right.\)
b/ \(\Delta=9-4\left(1+\sqrt{5}\right)\left(1-\sqrt{5}\right)=25\)
\(\Rightarrow\left\{{}\begin{matrix}x_1=\frac{3+\sqrt{25}}{2\left(1-\sqrt{5}\right)}=-1-\sqrt{5}\\x_2=\frac{3-\sqrt{25}}{2\left(1-\sqrt{5}\right)}=\frac{1+\sqrt{5}}{4}\end{matrix}\right.\)
\(a)4x^2-3\sqrt{3}x-6=0\)
Có: \(a=4;b=-3\sqrt{3};c=-6\)
\(\Delta=b^2-4ac\\ =\left(-3\sqrt{3}\right)^2-4.4.\left(-6\right)\\ =123>0\)
Phương trình có 2 nghiệm phân biệt:
\(x_1=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-\left(-3\sqrt{3}\right)+\sqrt{123}}{2.4}=\frac{3\sqrt{3}+\sqrt{123}}{8}\)
\(x_2=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-\left(-3\sqrt{3}\right)-\sqrt{123}}{2.4}=\frac{3-\sqrt{123}}{8}\)
\(b)\left(1-\sqrt{5}\right)x^2-3x+\sqrt{5}+1=0\)
Có: \(a=1-\sqrt{5};b=-3;c=\sqrt{5}+1\)
\(\Delta=b^2-4ac\\ =\left(-3\right)^2-4.\left(1-\sqrt{5}\right)\left(\sqrt{5}+1\right)\\ =25>0\)
Phương trình có 2 nghiệm phân biệt:
\(x_1=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-\left(-3\right)+\sqrt{25}}{2\left(1-\sqrt{5}\right)}=-1-\sqrt{5}\\ x_2=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-\left(-3\right)-\sqrt{25}}{2\left(1-\sqrt{5}\right)}=\frac{1+\sqrt{5}}{4}\)
