Question

Chứng minh

\(\frac{2\left(\sqrt{3}-1\right)}{4-2\sqrt{3}+1}=\frac{6\sqrt{3}+2}{13}\)

Answer 1

Cái này dễ mà, nhân lượng liên hợp là ra thui :v

Ta có

\(VT=\frac{2\left(\sqrt{3}-1\right)}{4-2\sqrt{3}+1}=\frac{2\sqrt{3}-2}{5-2\sqrt{3}}\\ =\frac{\left(2\sqrt{3}-2\right)\left(5+2\sqrt{3}\right)}{\left(5-2\sqrt{3}\right)\left(5+2\sqrt{3}\right)}\\ =\frac{10\sqrt{3}+\left(2\sqrt{3}\right)^2-10-4\sqrt{3}}{5^2-\left(2\sqrt{3}\right)^2}\\ =\frac{6\sqrt{3}+12-10}{25-12}\\ =\frac{6\sqrt{3}+2}{13}=VP\left(đpcm\right)\)