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    Question

    If a + b + c = 5, a³ + b³ + c³ = 95 and abc =15, then find the value of a² + b² + c² – ab –bc – ca

    A 20 Correct Answer Incorrect Answer
    B 10 Correct Answer Incorrect Answer
    C 15 Correct Answer Incorrect Answer
    D 25 Correct Answer Incorrect Answer

    Solution

    Given - a + b + c = 5 a³ + b³ + c³ = 95 abc =15 As we know that – a³ + b³ +c³ –3abc = (a+ b+ c) (a² + b² + c² -ab-bc-ca) 95 -3×15 = 5 (a² + b² + c² -ab-bc-ca) (95 -45)/5 = (a² + b² + c² -ab-bc-ca) (a² + b² + c² -ab-bc-ca) = 50/5 =10

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