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Question Number 137648 by JulioCesar last updated on 05/Apr/21

Commented by mr W last updated on 05/Apr/21

2+(√5)

2+5

Answered by mr W last updated on 05/Apr/21

x^4 +x^2 −((11)/5)=0 ⇒x^2 =((7(√5)−5)/( 10)) p=(((x+1)/(x−1)))^(1/3) +(((x−1)/(x+1)))^(1/3) p^3 =((x+1)/(x−1))+((x−1)/(x+1))+3p p^3 =2(1+(2/(x^2 −1)))+3p p^3 =2(1+(2/(((7(√5)−5)/( 10))−1)))+3p p^3 =2(7(√5)+16)+3p p^3 −3p−2(7(√5)+16)=0 p=2+(√5) (real root)

x4+x2−115=0⇒x2=75−510p=x+1x−13+x−1x+13p3=x+1x−1+x−1x+1+3pp3=2(1+2x2−1)+3pp3=2(1+275−510−1)+3pp3=2(75+16)+3pp3−3p−2(75+16)=0p=2+5(realroot)

Commented by JulioCesar last updated on 05/Apr/21

thank sir

thanksir

Commented by otchereabdullai@gmail.com last updated on 05/Apr/21

nice one!

niceone!

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