If x=√6+√5, then x2+1x2−2=
2√6
2√5
24
20
The correct option is D (20)
Given x=√6+√5 ......(i)
Applying reciprocal property,
Then 1x=1√6+√5=√6−√5(√6+√5)(√6−√5)
=√6−√5(√6)2−(√5)2=√6−√56−5
=√6−√51=
∴1x=√6−√5 ........(ii)
Now, consider x2+1x2−2=(x−1x)2
[Since, (a−b)2=a2+b2−2ab]
=[(√6+√5)−(√6−√5)]2
[From equations (i) and (ii)]
=(√6+√5−√6+√5)2=(2√5)2
=4×5=20
Hence, the value of the given expression is 20.