MathematicsLet  A=1-12α and B= β110,α,β∈R.  Let α1 be the value of α which satisfies  A+B2=A2+2222 and α2 be the value of α which satisfies A+B2=B2. Then α1-α2 is   equal to _____________.

Let  A=1-12α and B= β110,α,βR.  Let α1 be the value of α which satisfies  A+B2=A2+2222 and α2 be the value of α which satisfies A+B2=B2. Then α1-α2 is   equal to _____________.

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    Solution:

    A+B=β+103α A+B2=β+103αβ+103α =β+1203β+1+3αα2, A2=1-12α1-12α =-1-1-α2+2αα2-2 1-α+12α+4α2=β+1203α+β+1α2 α=1α1=1,  B2=β110β110 =β2+1ββ1=β+1203β+1+3αα2 β=0, α=-1=α2, α1-α2=1--1=2 

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