Question

If a= 5-2 root 6 then find the value of root a - 1/root a

Answer 1

2\sqrt2

Explanation:

a=5-2√6 ...(1)

`(1)/(a)=(1)/(5-2 √(6) ) *(5+2√(6) )/(5+2√(6) ) =(5+2√(6))/((5-2√(6))(5+2√(6))) =(5+2√(6))/(5 ^2-(2√(6))^2) =(5+2√(6))/(25-24) =5+2√(6)\\a+(1)/(a)=5-2√(6)+5+2√(6)=10`

`(√(a)-(1)/(√(a)))^2=(√(a))^2+((1)/(√(a)))^2-2 * √(a) * (1)/(√(a))=a+(1)/(a)-2=10-2=8\\√(a)-(1)/(√(a))=√(8)=2√(2)`