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Question

Let a, b, c be complex such that ab+bc+ca=12,(a+b+c)=2,abc=4 then the value of 1ab+c1+1bc+a1+1ac+b1 is


A

29

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B

19

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C

29

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D

19

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Solution

The correct option is A

29


ab+bc+ca=12;a+b+c=2;abc=4

1ab+c1+1bc+a1+1ac+b1=?

1ab+c1=1ab+[2ab]1 (a+b+c=2

=1abab+1

=1(a1)(b1)

1ab+c1+1bc+a1+1ac+b1

=1(a1)(b1)+1(c1)(b1)+1(a1)(c1)

=c1+b1+a1(a1)(b1)(c1)

=a3abcab+a1

=23412+21

=29


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