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If ax^(2)+bx+c =0 where ane0 is satisfied by alpha,beta,alpha^(2)andbeta^(2) where alphabetane0. Let set S be the set of all possible unordered pairs (alpha,beta). Then match the following lists: |
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Answer» `{:(,a,B,c,d),((1),q,s,s,r):}` (1) Let `alpha^(2)=alphaandbeta^(2)=beta`. `IMPLIES(alpha,beta)-=(1,1)` (ii) `alpha^(2)=betaandbeta^(2)=alpha` `impliesalpha^(4)=alpha` `impliesalpha(alpha^(3)-1)=0` `impliesalpha=0,1,(-1pmsqrt3i)/(2)` `implies(alpha,beta)-=((-1-sqrt3i)/(2),(-1+sqrt3i)/(2))` (iii) `alpha^(2)betaandbeta^(2)=beta(oralpha^(2)=alphaandbeta^(2)=alpha)` `impliesalpha^(2)=beta^(2)impliesalpha=pmbeta` `implies(alpha,beta)=(-1,1),(1,1)` Thus, possible unordered pairs `(alpha,beta)` such that that`alphabetane0` is `(1,1),(-1,1)or((-1-sqrt3i)/(2),(-1+sqrt3i)/(2))`. |
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