Question

prove that 2+√5 ÷2-√5 is irrational

​

Answer 1

Answer:

2+$\sqrt{5}$ x 2+$\sqrt{5}$ ÷2-$\sqrt{5\\}$ x 2+$\sqrt{5}$

=$(2+\sqrt{5} )^{2}$ ÷ $2^{2} - ( \sqrt{5} )^{2}$

=$2^{2} + 2$ x 2 x $\sqrt{5} + ( \sqrt{5} )^{2}$ ÷ $4 - 5$

=4 + 4$\sqrt{5}$ + 5 ÷ 1

= 9 +$4\sqrt{5}$ ⇒ is irrational