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Question Number 89795 by A8;15: last updated on 19/Apr/20

Answered by MJS last updated on 19/Apr/20

(x^2 +1)(x+1)^2 +x^2 =(x^2 +x+1)^2 x^2 (x^2 +1)+1=(x^2 −x+1)(x^2 +x+1) ⇒ ((x^2 +x+1)/(x^2 −x+1))=x+(1/x) x^4 −2x^3 +x^2 −2x+1=0 (x^2 −(√2)x−x+1)(x^2 +(√2)x−x+1)=0 and this is easy to solve

(x2+1)(x+1)2+x2=(x2+x+1)2x2(x2+1)+1=(x2−x+1)(x2+x+1)⇒x2+x+1x2−x+1=x+1xx4−2x3+x2−2x+1=0(x2−2x−x+1)(x2+2x−x+1)=0andthisiseasytosolve

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