If x=√6+√5 then (x−1x)2 = _______________.
20
24
25
36
x=√6+√5 ...(i)
1x=1√6+√5 Rationalizing factor of √6+√5 is √6−√5
∴1x=1√6+√5×√6−√5√6−√5
=√6−√56−5
=√6−√5 ...(ii)
∴x−1x=√6+√5−(√6−√5)
=√6+√5−√6+√5
=2√5 ∴(x−1x)2=(2√5)2
=20