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Question Number 157184 by cortano last updated on 20/Oct/21

p(x)=x^3 −3ax^2 +(3a^2 +1)x−(a^3 +a) p(2)<0 prove that 2<a<3

p(x)=x3−3ax2+(3a2+1)x−(a3+a) p(2)<0 provethat2<a<3

Answered by ghimisi last updated on 20/Oct/21

p(x)=x^3 −3ax^2 +3a^2 x−x^3 +x−a=(x−a)^3 +x−a p(2)<0⇒(2−a)[(2−a)^2 +1]<0⇒a>2 a<3 ??????

p(x)=x3−3ax2+3a2x−x3+x−a=(x−a)3+x−a p(2)<0⇒(2−a)[(2−a)2+1]<0⇒a>2 a<3??????

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