Question

if a+b+c = 10 and ab+bc+ca = 8 then find the value of a^2 + b^2 + c^2

Answer 1

Answer:

84

Step-by-step explanation:

${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2( ab+ bc+ ca) \\ {10}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + \: 2 \times 8 \\ 100 - 16 = {a}^{2} + {b}^{2} + {c}^{2} \\ {a}^{2} + {b}^{2} + {c}^{2} = 84$