Question

x + 1/x = 1 then x^8 + x^5 + X^3 + 1 = ?

Answer 1

hi,

if x+1/x=1 then x^8+x^5+x^3+1=0.

Indeed:

x+1/x=1==>(x+1/x)²=x²+1/x²+2=1²=1

==>x²+1/x²=-1

(x+1/x)^4=x^4+4x^3*1/x+6*x^2*1/x²+4/x²+1/x^4

1=x^4+1/x^4+4(x²+4/x²)+6

1=x^4+1/x^4+2

x^4+1/x^4=-1

x^8+x^5+x^3+1=x^4(x^4+x+1/x+1/x4)=x^4(-1+1)=0

Answer 2

solution

x + 1/x=1

by taking the L.C.M from the left hand side of the equation

1. ⇒ (x*x + 1)/x=1

1. x² + 1=x ⇒x²-x+1=0

1. by solving the equation x=1/2

1. then we put the value of x in to

1. (1/2)∧8 + (1/2)∧5 + (1/2)∧3 + 1

1. ⇒ 1/256 + 1/32 +1/8 +1

1. ⇒(1+8+32+256)/256=297/256

1. then the correct answer is 297/256