If a2 + b2 + 4c2 = 2(a + b - 2c) - 3 and a, b, c are real, then the value of (a2 + b2 + c2) is?
A. 3
B. $${\text{3}}\frac{1}{4}$$
C. 2
D. $${\text{2}}\frac{1}{4}$$
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & {a^2} + {b^2} + 4{c^2} = 2\left( {a + b - 2c} \right) - 3 \cr & \Rightarrow {a^2} + {b^2} + 4{c^2} - 2a - 2b + 4c + 3 = 0 \cr & \Rightarrow {a^2} - 2a + 1 + {b^2} - 2b + 1 + 4{c^2} + 4c + 1 = 0 \cr & \Rightarrow {\left( {a - 1} \right)^2} + {\left( {b - 1} \right)^2} + {\left( {2c + 1} \right)^2} = 0 \cr & \cr & \therefore a - 1 = 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a = 1 \cr & \,\,\,\,\,\,\,b - 1 = 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,b = 1 \cr & \,\,\,\,2c + 1 = 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,c = \frac{{ - 1}}{2} \cr & \cr & \therefore {a^2} + {b^2} + {c^2} \cr & \Rightarrow 1 + 1 + \frac{1}{4} \cr & \Rightarrow 2 + \frac{1}{4} \cr & \Rightarrow \frac{9}{4} \cr & \Rightarrow 2\frac{1}{4} \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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