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Question

If a2 – 2a – 1 = 0, then a2+1a2 = __________.

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Solution

Given:a2-2a-1=0a2-1=2aDividing 'a' on both sides, we geta2-1a=2aaa2a-1a=2a-1a=2Squaring both sides, we geta-1a2=22 a2+1a2-2a1a=4 Using the identity: a-b2=a2+b2-2aba2+1a2-2=4a2+1a2=6

Hence, if a2 – 2a – 1 = 0, then a2+1a2 = 6.

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