If a + b + c = 15 and ab + bc + ca = 30, find a 2 + b 2 + c 2 .

Question

If a + b + c = 15 and ab + bc + ca = 30, find a 2 + b 2 + c 2 .

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Isabella 2 weeks 2021-09-07T14:05:55+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-07T14:07:29+00:00

    Answer:

    (a+b+c)²=a²+b²+c²+2ab+2bc+2ac

    = (15)²=a²+b²+c²+2(ab+bc+ac)

    = 225=a²+b²+c²+2(30)

    = 225=a²+b²+c²+60

    = 225-60=a²+b²+c²

    = 165=a²+b²+c²

    0
    2021-09-07T14:07:41+00:00

    EXPLANATION.

    => a + b + c = 15

    => ab + bc + ca = 30

    To find a² + b² + c².

    according to the question,

    As we know that,

    Formula of ( a + b + c)²

    ( a + b + c)² = a² + b² + c² + 2 ( ab + bc

    + ca)

    put the value in above equation

    we get,

    => ( 15 )² = a² + b² + c² + 2 ( 30 )

    => 225 = a² + b² + c² + 60

    => 225 – 60 = a² + b² + c²

    => a² + b² + c² = 165

    Therefore,

    value of ( a² + b² + c² ) = 165

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