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 cosAa+cosBb+cosCc 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 B61144 From equation a + b + c = 13 ab + bc + ca = 54 abc = 72 cosAa+cosBb+cosCc =b2+c2−a22abc+a2+c2−b22abc+a2+b2−c22abc =(a+b+c)2−2(ab+bc+ca)2abc=61144