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Question

If a+1a=174; Find (a-1a)


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Solution

Step 1: Squaring both sides in the given equation

Given equation: a+1a=174

On Squaring both sides, we get,

a+1a2=1742

a2+1a2+2=28916 ( As a+b2=a2+b2+2ab )

a2+1a2=28916-2 ( Transposing 2from left side to right side and while doing so addition becomes subtraction )

a2+1a2=289-3216 ( Taking LCM of Right side part and solving further )

a2+1a2=25716----------- (i)

Step 2: Now, Squaring a-1a

a-1a2=a2+1a2-2 ( As a-b2=a2+b2-2ab)

a-1a2=25716-2 ( Substituting the value of a2+1a2from (i) )

a-1a2=257-3216( Taking LCM of Right side part and solving further )

a-1a2=22516

Taking square root on both sides,

a-1a2=22516

a-1a=154

Hence, the value of a-1ais 154.


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