Question

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

• A. 216, -216
• B. 36,-36
• C. 6,- 6
• D. 12, -12

Answer 1

Answer:

A. 216, -216

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

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

Now,

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

a + b + c = +6 , -6

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