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Question Number 161295 by Ari last updated on 15/Dec/21

prove that:x^8 +x^6 −x^3 −x+1>0,x∈R

provethat:x8+x6−x3−x+1>0,x∈R

Commented byAri last updated on 15/Dec/21

thanks Mr!

Commented bymr W last updated on 15/Dec/21

=x^8 −x^4 +(1/4)+x^6 −x^3 +(1/4)+x^4 −x^2 +(1/4)+x^2 −x+(1/4) =(x^4 −(1/2))^2 +(x^3 −(1/2))^2 +(x^2 −(1/2))^2 +(x−(1/2))^2 >0

=x8−x4+14+x6−x3+14+x4−x2+14+x2−x+14 =(x4−12)2+(x3−12)2+(x2−12)2+(x−12)2 >0

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