If m+1m=5, find the value of m2+1m2.
23
To find the value of (m2+1m2) apply the identity (a+b)2=a2+b2+2ab
⇒(m2+1m2)=(m+1m)2−2m×1m [Here, a=m,b=1m]
Given, m+1m=5
Substituting value of m+1m=5 in the above equation,
We get m2+1m2=(5)2−(2mm)
=25−2 [2mm=2 by cancelling m in numerator and denominator]
=23