Question

1) 3x² - 2√3x -13=0.

2) x² - 2 (√3 + √2 ) x+4√6 =0.

3) √2x² - 2 (√3 -1) x - 3√2 =0.

Answer 1

1: \(\Delta=\left(-2\sqrt{3}\right)^2-4\cdot3\cdot\left(-13\right)=168>0\)

Pt có hai nghiệm phân biệt là:

\(\left\{{}\begin{matrix}x=\dfrac{2\sqrt{3}-2\sqrt{42}}{6}=\dfrac{\sqrt{3}-\sqrt{42}}{6}\\x=\dfrac{\sqrt{3}+\sqrt{42}}{6}\end{matrix}\right.\)

2: \(\Delta=\left(2\sqrt{3}+2\sqrt{2}\right)^2-16\sqrt{6}\)

\(=12+8+16\sqrt{6}-16\sqrt{6}=20\)

=>PT có 2 nghiệm phân biệt là:

\(\left\{{}\begin{matrix}x=\dfrac{2\sqrt{3}+2\sqrt{2}-2\sqrt{5}}{2}=\sqrt{3}+\sqrt{2}-\sqrt{5}\\x=\sqrt{3}+\sqrt{2}+\sqrt{5}\end{matrix}\right.\)