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Question

If a+b+c=6, 1a+1b+1c=32, then ab+ac+ba+bc+ca+cb=__________.

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Solution

Given:1a+1b+1c=32 ...1a+b+c=6 ...2Now,ab+ac+ba+bc+ca+cbAdding and subtracting 3, we get=ab+ac+ba+bc+ca+cb+3-3=ab+ac+ba+bc+ca+cb+1+1+1-3=ab+ac+ba+bc+ca+cb+aa+bb+cc-3=aa+ba+ca+ab+bb+cb+ac+bc+cc-3=a+b+ca+a+b+cb+a+b+cc-3=6a+6b+6c-3 From 2=6a+6b+6c-3 =61a+1b+1c-3=632-3 From 1=9-3=6

Hence, if a+b+c=6, 1a+1b+1c=32, then ab+ac+ba+bc+ca+cb=6.

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