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Question Number 218103 by ArshadS last updated on 29/Mar/25

x+(1/x)=3 , x^5 +(1/x^5 )=?

x+1x=3,x5+1x5=?

Answered by Rasheed.Sindhi last updated on 29/Mar/25

x+(1/x)=3 , x^5 +(1/x^5 )=? ▶(x+(1/x)=3)^2 x^2 +(1/x^2 )=7 ▶(x+(1/x)=3)^3 x^3 +(1/x^3 )+3(x+(1/x))=27 x^3 +(1/x^3 )=18 ▶(x^2 +(1/x^2 ))(x^3 +(1/x^3 ))=126 x^5 +(1/x^5 )+x+(1/x)=126 x^5 +(1/x^5 )+3=126 x^5 +(1/x^5 )=123

x+1x=3,x5+1x5=?▸(x+1x=3)2x2+1x2=7▸(x+1x=3)3x3+1x3+3(x+1x)=27x3+1x3=18▸(x2+1x2)(x3+1x3)=126x5+1x5+x+1x=126x5+1x5+3=126x5+1x5=123

Answered by Rasheed.Sindhi last updated on 29/Mar/25

x+(1/x)=3 , x^5 +(1/x^5 )=? x^2 =3x−1⇒x^4 =9x^2 −6x+1 =9(3x−1)−6x+1 =21x−8 ⇒x^5 =21x^2 −8x=21(3x−1)−8x=55x−21 (1/x)=3−x⇒(1/x^2 )=x^2 −6x+9 ⇒(1/x^3 )=x−6+(9/x)=x−6+9(3−x)=−8x+21 ⇒(1/x^4 )=−8+((21)/x)=−8+21(3−x)=55−21x ⇒(1/x^5 )=((55)/x)−21=55(3−x)−21=144−55x x^5 +(1/x^5 )=55x−21+144−55x=123

x+1x=3,x5+1x5=?x2=3x−1⇒x4=9x2−6x+1=9(3x−1)−6x+1=21x−8⇒x5=21x2−8x=21(3x−1)−8x=55x−211x=3−x⇒1x2=x2−6x+9⇒1x3=x−6+9x=x−6+9(3−x)=−8x+21⇒1x4=−8+21x=−8+21(3−x)=55−21x⇒1x5=55x−21=55(3−x)−21=144−55xx5+1x5=55x−21+144−55x=123

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