Question

Giải phương trình sau

\(x^2-\left(\sqrt{2}+\sqrt{3}\right)x+\sqrt{6}-3\sqrt{2}+3\sqrt{3}-9=0\)

Answer 1

\(\sqrt{6}- 3\sqrt{2}+3\sqrt{3}-9\)

\(=\sqrt{2}\left(\sqrt{3}-3\right)+3\left(\sqrt{3}-3\right)=\left(\sqrt{2}+3\right)\left(\sqrt{3}-3\right)\)

\(\Rightarrow x^2-\left(\sqrt{2}+\sqrt{3}\right)x+\left(\sqrt{2}+3\right)\left(\sqrt{3}-3\right)=0\)

\(\Delta=\left(\sqrt{2}+\sqrt{3}\right)^2-4\left(\sqrt{2}+3\right)\left(\sqrt{3}-3\right)\)

\(\Delta=2+3+2\sqrt{6}-4\sqrt{6}+12\sqrt{2}-12\sqrt{3}-36\)

\(\Delta=5-2\sqrt{6}+12\left(\sqrt{2}-\sqrt{3}\right)-36\)

\(\Delta=-31-2\sqrt{6}+12\left(\sqrt{2}-\sqrt{3}\right)< 0\)

Phương trình vô nghiệm