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Given a+b+c=7 and a^2+b^2+c^2=25 Find (a+b) ^2 + (a+c) ^2 + (b+c) ^2

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  1. 1 July, 09:52
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    26.

    Step-by-step explanation:

    (a + b) ^2 + (a + c) ^2 + (b + c) ^2 = a^2 + b^2 - 2 ab + a^2 + c^2 - 2ac + b^2 + c^2 - 2bc

    = 2 (a^2 + b^2 + c^2) - 2 (ab + ac + bc)

    = 50 - 2 (ab + ac + bc) ... (1).

    (a + b + c) ^2 = a^2 + ab + ac + ab + b^2 + bc + ac + bc + c^2

    = a^2 + b^2 + c^2 + 2 (ab + ac + bc)

    = 25 + 2 (ab + ac + bc)

    But (a + b + c) ^2 = 7^2 = 49. So:-

    49 = 25 + 2 (ab + ac + bc)

    2 (ab + ac + bc) = 49 - 25 = 24.

    Substituting for this in (1) above:

    (a + b) ^2 + (a + c) ^2 + (b + c) ^2 = 50 - 24 = 26 (answer).
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