Question 103

If $$a^{2} + b^{2} + c^{2} + 3 = 2 (a- b - c)$$, then the value of $$2 a - b + c$$ is :

Solution

Expression : $$a^{2} + b^{2} + c^{2} + 3 = 2 (a- b - c)$$

=> $$(a^2 - 2a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$$

=> $$(a-1)^2 + (b+1)^2 + (c+1)^2 = 0$$

$$\therefore$$$$ a-1 = 0 => a = 1$$

and $$b+1 = 0 => b = -1$$

and $$c+1 = 0 => c = -1$$

To find : $$2a - b + c$$

= $$2*1 - (-1) + (-1)$$

= $$2 + 1 - 1 = 2$$

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