Applying the formula, (a−b)2=a2+b2−2ab(m−1m)2=m2+(1m)2−2m×1m=m2+1m2−2=>m2+1m2=(m−1m)2+2Substituting m−1m=5, =>m2+1m2=52+2=25+2=27
Squaring both sides,
(m2+1m2)2=27×27=729
m4+1m4+2×m2×(1m2)=729
If m−1m=5, find :
(i) m2+1m2
(ii) m4+1m4
(iii) m2−1m2