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    Question

    If a + b + c = 5, a³ + b³ + c³ = 85 and abc =25, then

    find the value of a² + b² + c² – ab –bc – ca
    A 12 Correct Answer Incorrect Answer
    B 2 Correct Answer Incorrect Answer
    C 8 Correct Answer Incorrect Answer
    D 14 Correct Answer Incorrect Answer

    Solution

    Given - a + b + c = 5 a³ + b³ + c³ = 85 abc =25 As we know that – a³ + b³ +c³ –3abc = (a+ b+ c) (a² + b² + c² -ab-bc-ca) 85 -3×25 = 5 (a² + b² + c² -ab-bc-ca) (85 -75)/5 = (a² + b² + c² -ab-bc-ca) (a² + b² + c² -ab-bc-ca) = 10/5 =2

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