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
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Correct Answer: 27
Solution : Given: If $a+b+c=9$ (where $a,b,c$ are real numbers). For the minimum value, $a=b=c$ ⇒ $3a = 9$ ⇒ $a = \frac{9}{3}=3$ 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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