If (a+b)=6, and ab=2, then the value of 1a2+1b2 is equal to
8
Given (a+b)=6
Squaring both sides we get
(a+b)2=36
a2+b2+2ab=36
a2+b2+2×2=36 (as ab=2)
a2+b2=36−4
a2+b2=32 . . . (1)
The given expression is
1a2+1b2
=a2+b2a2b2
=(a+b)2−2aba2b2
=(6)2−2×(2)(2)2
=36−44
=8