Giải phương trình: x² - √3.x - 2 - √6 = 0

x = - √2 hoặc x = √2 + √3

\(x^2-\sqrt{3}.x-2-\sqrt{6}=0\)

<=> \(x^2+x\sqrt{2}-x\sqrt{3}-\sqrt{6}-x\sqrt{2}-2=0\)

<=>\(x\left(x+\sqrt{2}\right)-\sqrt{3}\left(x+\sqrt{2}\right)-\sqrt{2}\left(x+\sqrt{2}\right)=0\)

<=> \(\left(x+\sqrt{2}\right)\left(x-\sqrt{3}-\sqrt{2}\right)=0\)

<=> \(x=-\sqrt{2}\) hoặc \(x=\sqrt{3}+\sqrt{2}\)

x² - √3.x - 2 - √6 = 0

<=> x² + √2.x - √2.x - 2 - √3.x - √6 = 0

<=> x(x + √2) - √2(x + √2) - √3(x + √2) = 0

<=> (x + √2).(x - √2 - √3) = 0

<=> x = - √2 hoặc x = √2 - √3