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If $a^{2} +$ $b^{2}$ + $c^{2}$ = 16 and ab + bc + ca = 10, find a + b + c.

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answer is C.

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Detailed Solution

Given,

a^{2} + b^{2} + c^{2}

= 16 and ab + bc + ca = 10
Find a + b + c =?
We know that

{(a + b + c)}^{2}

a^{2} + b^{2} + c^{2}

+ 2(ab + bc + ca)
Putting the given values in this equation,
⇒

{(a + b + c)}^{2}

=16 + 2 (10)
⇒

{(a + b + c)}^{2}

=16 + 20 = 36
Now, on removing the square-root we get,

⇒ a + b + c =

\sqrt{36}

= ±6
Here we are only taking positive value as the answer because every non-negative real number has a unique non-negative square-root, called the principal square-root.
Hence, 6 is the right answer.
So, option 2 is correct.

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