one liner

6
u said one liner so .....lafda kara

did virtually

tellmeh if wrng i'll try:P

edited d post meine x>0 dekha ni tha

we know the

x+1/x≥1 (AM>GM)
--------
2

x + 1/x ≥2

similarly we get the min value of x⁶+1/x⁶≥2

so min value is

[2⁶-2-2]/[8+2]
so the answer is

6

better approach:

put (x+1/x)³=a
and x³+1/x³=b

the expression becomes
a²-b²/a+b
=> a+b
=> 3(x+1/x)

we know that x+1/x≥2
=> expression has min value equal to 6

which is possible when x=1(becoz then only AM=GM)

yeah thats 6 ...............sorry ..........i took x=-1............dekha ni ki x>0

so best approach .put x=1

yeah thats good for objective papers...[1][1]