Let A = 1 - 1 2 α and B = β 1 1 0 , α , β ∈ R . Let α 1 be the value of α which satisfies A + B 2 = A 2 + 2 2 2 2 and α 2 be the value of α which satisfies A + B 2 = B 2 . Then α 1 - α 2 is equal to

Step-by-step solution

Given A = 1 - 1 2 α and B = β 1 1 0 , α , β ∈ R , So, A + B = β + 1 0 3 α Now A + B 2 = β + 1 0 3 α β + 1 0 3 α = β + 1 2 0 3 β + 1 + 3 α α 2 Also, A 2 = 1 - 1 2 α 1 - 1 2 α = - 1 - 1 - α 2 + 2 α α 2 - 2 Now solving A + B 2 = A 2 + 2 2 2 2 ⇒ β + 1 2 0 3 α + β + 1 α 2 = 1 - α + 1 2 α + 4 α 2 Now on comparing both side we get, α = 1 = α 1 And B 2 = β 1 1 0 β