Question : If $a + b + c = 9$ (where $a, b, c$ are real numbers), the minimum value of $a^{2} + b^{2} + c^{2}$ is:
Option 1: 100
Option 2: 9
Option 3: 27
Option 4: 81

Question

Question : If $9 a + 9 b + 9 c = 81$ and $4 a b + 4 b c + 4 c a = 160$ , then what is the value of $6 a^{2} + 6 b^{2} + 6 c^{2}$ ?

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Answer 1

Correct Answer: 27

Solution : Given: If $a + b + c = 9$ (where $a, b, c$ are real numbers).
For the minimum value,
$a = b = c$
⇒ $3 a = 9$
⇒ $a = \frac{9}{3} = 3$
Similarly, $b = 3$ and $c = 3$
Replacing $a$ , $b$ , and $c$ with their values, the equation, $a + b + c = 9$ , is satisfied.
So, the minimum value of ( $a^{2} + b^{2} + c^{2}$ ) is $3^{2} + 3^{2} + 3^{2}$ = 27.
Hence, the correct answer is 27.

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Question : If a+b+c=9 (where a,b,c are real numbers), the minimum value of a2+b2+c2 is:Option 1: 100Option 2: 9Option 3: 27Option 4: 81

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Question : If $a + b + c = 9$ (where $a, b, c$ are real numbers), the minimum value of $a^{2} + b^{2} + c^{2}$ is:
Option 1: 100
Option 2: 9
Option 3: 27
Option 4: 81