Multiple Choice QuestionsIf a2 + b2 + 4c2 = 2(a + b - 2c) - 3 and a, b, c are real, then the value of (a2 + b2 + c2) is
2
3
C.
a2 + b2 + 4c2 = 2(a + b - 2c) - 3
⟹ a2 + b2 + 4c2 = 2a + 2b - 4c - 3
⟹ (a2 - 2a + 1) + (b2 - 2b + 1) + (4c2 + 4c + 1) - 1 - 1 - 1 = -3
⟹ (a - 1)2 + (b - 1)2 + (2c + 1)2 = 0
Hence,
(a - 1) = 0 ⟹ a = 1
(b - 1) = 0 ⟹ b = 1
(2c + 1) = 0 ⟹ c =-1/2
If x ≠ 0, y ≠ 0 and z ≠ 0 and 
, then the relation among x, y and z is
x = y = z
x + y + z = 0
x + y = z
If x2 + y2 + z2 = 2(x - y - z) - 3, then the value of 2x - 3y + 4z is (assume that x, y and z) are all real numbers).
3
0
9
1
then the value of 
is
is
is
Switch
is
then the value of 12 * 4 is
then the value of abc is
