Question

Tính: \(\dfrac{2\left(\sqrt{6-2\sqrt{5}}+6-2\sqrt{5}+1\right)}{\sqrt{6-2\sqrt{5}}}\)

Giúp mình vs, tks nhiều 🌹

Answer 1

\(\dfrac{2\left(\sqrt{6-2\sqrt{5}}+6-2\sqrt{5}+1\right)}{\sqrt{6-2\sqrt{5}}}\)

\(=\dfrac{2\left[\left(\sqrt{\sqrt{5^2}-2\sqrt{5}+1}\right)+6-2\sqrt{5}+1\right]}{\sqrt{5^2-2\sqrt{5}+1}}\)

\(=\dfrac{2\left[\sqrt{\left(\sqrt{5}-1\right)^2}+6-2\sqrt{5}+1\right]}{\sqrt{\left(\sqrt{5}-1\right)^2}}\)

\(=\dfrac{2\left(\left|\sqrt{5}-1\right|+6-2\sqrt{5}+1\right)}{\left|\sqrt{5}-1\right|}\)

\(=\dfrac{2\left(\sqrt{5}-1+6-2\sqrt{5}+1\right)}{\sqrt{5}-1}\)

\(=\dfrac{2\left(-\sqrt{5}+6\right)}{\sqrt{5}-1}\)

#Ayumu