a.\(x^2-\left(2\sqrt{2}+1\right)x+2\sqrt{2}=0\)
\(\Delta=\left[-\left(2\sqrt{2}+1\right)\right]^2-4.\left(2+\sqrt{2}\right)\)
\(=8+4\sqrt{2}+1-8-4\sqrt{2}=1>0\)
=> pt có 2 nghiệm
\(\left\{{}\begin{matrix}x_1=\dfrac{2\sqrt{2}+1+\sqrt{1}}{2}=1+\sqrt{2}\\x_2=\dfrac{2\sqrt{2}+1-\sqrt{1}}{2}=\sqrt{2}\end{matrix}\right.\)
b.\(x^2-2\left(\sqrt{5}+1\right)x-15-2\sqrt{5}=0\)
\(\Delta=\left[-2\left(\sqrt{5}+1\right)\right]^2-4.\left(-15-2\sqrt{5}\right)\)
\(=4\left(5+2\sqrt{5}+1\right)+60+8\sqrt{5}\)
\(=20+8\sqrt{5}+4+60+8\sqrt{5}=84+16\sqrt{5}>0\)
=> pt có 2 nghiệm
\(\left\{{}\begin{matrix}x_1=\dfrac{2\left(\sqrt{5}+1\right)+\sqrt{84+16\sqrt{5}}}{2}\\x_2=\dfrac{2\left(\sqrt{5}+1\right)-\sqrt{84+16\sqrt{5}}}{2}\end{matrix}\right.\)
