If x=√6+√5, then x2+1x2−2=
2√6
2√5
24
20
x=√6+√5
Then 1x=1√6+√5=√6−√5(√6+√5)(√6−√5)
=√6−√5(√6)2−(√5)2=√6−√56−5
=√6−√51=√6−√5
Now, x2+1x2−2=(x−1x)2
=[(√6+√5)−(√6−√5)]2
=(√6+√5−√6+√5)2=(2√5)2
=4×5=20