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Question Number 195121 by mathlove last updated on 25/Jul/23

x^2 −x−1=0 x^8 +2x^7 −47x=?

x2−x−1=0x8+2x7−47x=?

Answered by qaz last updated on 25/Jul/23

x^8 +2x^7 −47x =x^6 (x^2 −x)+3x^7 −47x =3x^5 (x^2 −x)+4x^6 −47x =4x^4 (x^2 −x)+7x^5 −47x =7x^3 (x^2 −x)+11x^4 −47x =11x^2 (x^2 −x)+18x^3 −47x =18x(x^2 −x)+29x^2 −47x =29(x^2 −x)+47x−47x=29

x8+2x7−47x=x6(x2−x)+3x7−47x=3x5(x2−x)+4x6−47x=4x4(x2−x)+7x5−47x=7x3(x2−x)+11x4−47x=11x2(x2−x)+18x3−47x=18x(x2−x)+29x2−47x=29(x2−x)+47x−47x=29

Answered by Rasheed.Sindhi last updated on 25/Jul/23

x^2 −x−1=0 , x^8 +2x^7 −47x=? ⇒x^2 =x+1 ⇒x^3 =x^2 +x=(x+1)+x=2x+1 ⇒x^4 =2x^2 +x=2(x+1)+x=3x+2 ⇒x^7 =x^3 ∙x^4 =(2x+1)(3x+2)=6x^2 +7x+2=6(x+1)+7x+2=13x+8 ⇒x^8 =13x^2 +8x=13(x+1)+8x=21x+13 x^8 +2x^7 −47x=(21x+13)+2(13x+8)−47x) =21x+26x−47x+13+16=29

x2−x−1=0,x8+2x7−47x=?⇒x2=x+1⇒x3=x2+x=(x+1)+x=2x+1⇒x4=2x2+x=2(x+1)+x=3x+2⇒x7=x3⋅x4=(2x+1)(3x+2)=6x2+7x+2=6(x+1)+7x+2=13x+8⇒x8=13x2+8x=13(x+1)+8x=21x+13x8+2x7−47x=(21x+13)+2(13x+8)−47x)=21x+26x−47x+13+16=29

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