Question

if x=5+2root 6 show that root x+1/rootx=2root 3

Answer 1

X=5-2√6
=3+2-2√3√2
=(√3)²-2√3√2+(√2)²
=(√3-√2)²
∴, x=√3-√2
∴, 1/x
=1/√3-√2
=(√3+√2)/(√3-√2)(√3+√2)
=(√3+√2)/{(√3)²-(√2)}
=(√3+√2)/(3-2)
=√3+√2
∴, √x+1/√x
=√3-√2+√3+√2
=2√3