If $$a^2+b^2+4c^2=2(a+b-2c-3)$$ and a, b, c are real, then the value of $$(a^2+b^2+c^2)$$ is ?->(Show Answer!)

1. If $$a^2+b^2+4c^2=2(a+b-2c-3)$$ and a, b, c are real, then the value of $$(a^2+b^2+c^2)$$ is

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By: anil on 05 May 2019 01.55 am

$$a^2+b^2+4c^2=2(a+b-2c-3)$$
So, $$(a-1)^2+(b-1)^2+(2c+1)^2=0$$
Or, $$a=1,b=1,c=frac{-1}{2}$$
So, $$a^2+b^2+c^2=1+1+frac{1}{4}=frac{9}{4}$$

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