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Question Number 184424 by Fridunatjan08 last updated on 06/Jan/23
Help please: { ((x+x^(−1) −(√2)=0)),((x^(2017) +x^(2017) +(√2)=?)) :}
Helpplease:{x+x−1−2=0x2017+x2017+2=?
Commented by Rasheed.Sindhi last updated on 06/Jan/23
x^(2017) +x^(−2017) +(√2)=? ?
x2017+x−2017+2=??
Answered by Rasheed.Sindhi last updated on 06/Jan/23
{ ((x+x^(−1) −(√2)=0)),((x^(2017) +x^(−2017) +(√2)=?)) :} x(x+x^(−1) −(√2) =0)⇒x^2 =(√2) x−1 x^3 =(√2) x^2 −x=(√2) ((√2) x−1)−x=x−(√2) x^4 =x^2 −(√2) x=(√2) x−1−(√2) x=−1 x^(2017) +x^(−2017) +(√2) =(x^4 )^(504) x+(x^4 )^(−504) x^(−1) +(√2) =(−1)^(504) x+(−1)^(−504) x^(−1) +(√2) =x+x^(−1) +(√2) =(√2) +(√2) =2(√(2 ))✓
{x+x−1−2=0x2017+x−2017+2=?x(x+x−1−2=0)⇒x2=2x−1x3=2x2−x=2(2x−1)−x=x−2x4=x2−2x=2x−1−2x=−1x2017+x−2017+2=(x4)504x+(x4)−504x−1+2=(−1)504x+(−1)−504x−1+2=x+x−1+2=2+2=22✓
Answered by mr W last updated on 06/Jan/23
x+(1/x)=(√2) ⇒x^2 +(1/x^2 )+2=2 ⇒x^2 +(1/x^2 )=0 ⇒x^4 =−1 x^(2017) +(1/x^(2017) )+(√2) =(x^4 )^(504) x+(1/((x^4 )^(504) x))+(√2) =x+(1/x)+(√2) =(√2)+(√2) =2(√2)
x+1x=2⇒x2+1x2+2=2⇒x2+1x2=0⇒x4=−1x2017+1x2017+2=(x4)504x+1(x4)504x+2=x+1x+2=2+2=22

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