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Let Delta = |{:(-bc,,b^(2)+bc,,c^(2)+bc)...

Let `Delta = |{:(-bc,,b^(2)+bc,,c^(2)+bc),(a^(2)+ac,,-ac,,c^(2)+ac),(a^(2)+ab,,b^(2)+ab,,-ab):}|` and the equation
`px^(3) +qx^(2) +rx+s=0` has roots a,b,c where `a,b,c in R^(+)`
`" if " Delta =27 " and " a^(2) +b^(2)+c^(2) =3`then

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The correct Answer is:
`0.50`
`Delta=abc|((-bc)/(a),b+c,c+b),(a+c,(-ac)/(b),c+a),(a+b,a+b,(-ab)/(c))|" , "Delta=(abc)/(abc)|(-bc,ab+ac,ac+ab),(ab+bc,-ac,bc+ab),(ac+bc,ac+bc,-ab)|`
`Delta=|(-b,ab+ac,ac+ab),(ab+bc,-ac,ab+bc),(ac+bc,ac+bc,-ab)|" , "Delta=|(-bc-ab-ac,0,ac+ab),(ab+bc+ac,-ab-bc-ac,ab+bc),(0,ab+bc+ac,-ab)|{:(C_(1)rarrC_(1)-C_(2)),(C_(2)rarrC_(2)-C_(3)):}`
`=(ab+bc+ac)^(2)|(-1,0,ac+ab),(1,-1,ab+bc),(0,1,-ab)|R_(1)rarrR_(1)+R_(2)+R_(3)`
`Delta=(ab+bc+ac)^(3)=37`
`ab+bc+ac=3,a^(2)+c^(2)+b^(2)=2`
`a+b+c=(-q)/(p),(a+b+c)^(2)=(q^(2))/(p^(2)),2+2xx3=(q^(2))/(p^(2))rArr(q^(2))/(p^(2))=9,(p)/(q)=(-1)/(2sqrt2),(sqrt2p)/(q)+1=(1)/(2)`
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