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Question

If m1m=5, then find m4+1m4

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Solution

Applying the formula, (ab)2=a2+b22ab
(m1m)2=m2+(1m)22m×1m=m2+1m22
=>m2+1m2=(m1m)2+2
Substituting m1m=5,
=>m2+1m2=52+2=25+2=27

Squaring both sides,

(m2+1m2)2=27×27=729

m4+1m4+2×m2×(1m2)=729

m4+1m4+2=729
m4+1m4=727

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