Question

If a + b + c =9, ab = 6, bc = 12, and ac = 8, then find
the value of a2 + b2 + c2​

Answer 1

Answer:

29

Explanation:

$(a + b + c )^{2} = {a}^{2} + {b}^{2} + {c}^{2} +2(ab + bc + ac) \\ \\ given \: a + b + c = 9 \: therefore \\ \\ {9}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(6 + 12 + 8) \\ \\ {9}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(26) \\ \\ 81 - 52 = {a}^{2} + {b}^{2} + {c}^{2} \\ \\ 29 = {a}^{2} + {b}^{2} + {c}^{2}$

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