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Question

If the sides a, b, c of a triangle ABC are the roots of the equation x3−13x2+54x−72=0, then the value of cos Aa+cos Bb+cos Cc is equal to

A
59144
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B
61144
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C
6172
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D
325
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Solution

The correct option is B 61144
From equation
a + b + c = 13
ab + bc + ca = 54
abc = 72
cosAa+cosBb+cosCc
=b2+c2a22abc+a2+c2b22abc+a2+b2c22abc
=(a+b+c)22(ab+bc+ca)2abc=61144

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