Question

please solve this question

Answer 1

$a + b + c = 12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( \: \bold{ \: given} \: \: )\\ \\ \\ \bold{ \underline{ \: square \: on \: both \: sides}} \\ \\ \\ \\ {(a + b + c)}^{2} = {12}^{2} \\ \\ \\ { a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) = 144 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \:( {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc \: + ca) } \: ) \\ \\ \\64 + 2(ab + bc + ca) = 144 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \: given \: \: {a}^{2} + {b}^{2} + {c}^{2} = 64}$




2( ab + bc + ca ) = 144 - 64

2( ab + bc + ca ) = 80

$ab + bc + ca = \frac{80}{2}$


ab + bc + ca = 40








Hence,

$\boxed{ \bold{ \underline{ \: ab + bc + ca = 40}}}$