If $a^2 + b^2 + c^2 = 14$ and$ ab + bc + ca = 11$, find $(a + b + c)^3=$.

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If $a^2 + b^2 + c^2 = 14$ and $ab + bc + ca = 11$ , find $(a + b + c)^3=$ .

A216, -216

B36,-36

C6,- 6

D12, -12

Answer:

$(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$

$a^2 + b^2 + c^2 = 14$
$ab + bc + ca = 11$

Now,

$(a + b + c)^2 = 14 + 2 \sqrt{ 11}= 36$

a + b + c = +6 , -6

$(a + b + c)^3 = 216 , -216$

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