Question

If a + b c = 7 and ab- bc - ca = 14
, find the value of a^2 +b^2 +c^2​

Answer 1

Answer:

${a}^{2} + {b}^{2} + {c}^{2} = 21$

Step-by-step explanation:

${a + b - c}^{2} \: = {a}^{2} + {b}^{2} + ({-c}^{2}) + 2ab - 2bc - 2ac \\ = > {7}^{2} = { a}^{2} + {b}^{2} + {c}^{2} + 2(ab - bc - ac) \\ = > 49 = { a}^{2} + {b}^{2} + {c}^{2} + 2(14) \\ = > { a}^{2} + {b}^{2} + {c}^{2} = 49 - 28 = 21$