a: \(\dfrac{5+2\sqrt{5}}{\sqrt{5}+\sqrt{2}}=\dfrac{\left(5+2\sqrt{5}\right)\left(\sqrt{5}-\sqrt{2}\right)}{3}=\dfrac{5\sqrt{5}-5\sqrt{2}+10-2\sqrt{10}}{3}\)

b: \(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}=\sqrt{\left(2-\sqrt{3}\right)^2}=2-\sqrt{3}\)

\(\dfrac{1}{1-\sqrt{5}}+\dfrac{1}{\sqrt{5}-1}=\dfrac{-1+1}{\sqrt{5}-1}=\dfrac{0}{\sqrt{5}-1}=0\)

\(\dfrac{1}{1-\sqrt{5}}+\dfrac{1}{\sqrt{5}-1}=\dfrac{1}{1-\sqrt{5}}-\dfrac{1}{1-\sqrt{5}}=0\)

a) \(\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\)

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

\(=\sqrt{5}-\sqrt{2}+\sqrt{5}+\sqrt{2}\)

\(=\sqrt{5}+\sqrt{5}\)

\(=2\sqrt{5}\)

b) \(\sqrt{\left(\sqrt{2}-1\right)^2}-\sqrt{\left(\sqrt{2}-5\right)^2}\)

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

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

\(=\sqrt{2}-1-5+\sqrt{2}\)

\(=2\sqrt{2}-6\)

\(\left(3+\frac{\sqrt{5}}{\sqrt{10}}+\sqrt{3}+\sqrt{5}\right)-\left(3-\frac{\sqrt{5}}{\sqrt{10}}+\sqrt{3}-\sqrt{5}\right)=\sqrt{34.64911064}\)

Cho hàm số y=(1-√5)x-1
a, Hàm số đồng biến hay nghịch biến trên R?vì sao
Hàm số nghịch biến vi (1-√5<0
b,Tính y khi x=1+√5
y=(1-√5)(1+√5)-1
y = -5