Question

If $a, b, c$ are real numbers such that $(a-2)^{2}+(b-2)^{2}+(c-2)^{2}=0$, then ________.

• A. $a, b, c$ are in G.P. and $a+b+c=6$
• B. $a, b, c$ are in G.P. and $a+b+c=4$
• C. $a, b, c$ are not in G.P.
• D. $a, b, c$ are in G.P. and $a+b+c=8$
• E. $a, b, c$ are not in G.P. and $a+b+c=16$

Hint:

$x^2+y^2+z^2=0 \implies x=y=z=0$.

Answer 1

The Correct Option is A

Step 1: Concept
If the sum of squares of real numbers is zero, each number must be zero.

Step 2: Meaning
$(a-2)=0, (b-2)=0, (c-2)=0 \implies a=2, b=2, c=2$.

Step 3: Analysis
$a, b, c = 2, 2, 2$. These are in G.P. (common ratio $r=1$).

Step 4: Conclusion
$a+b+c = 2+2+2 = 6$. Final Answer: (A)