Question

given that x*(x+1)=1, then find the value of (x+1)^3+1/(x+1)^3​

Answer 1

Answer:

we have, x+1/x=1

Or,x²+1=x

Or,x² -x+1=0

Or, x² -2.x.(1/2)+1/4=1/4 -1

Or,(x-1/2)²=-3/4

Or,x-1/2=±i√3/2

Or,x=1/2±i√3/2

For x=1/2+i√3/2

x+1=1+1/2+i√3/2

Or,x+1=3/2+i√3/2

Or,(x+1)³ =(1/8)(3+i√3)³

Or, (x+1)³=(1/8)(27+i27√3–27-i3√3)

Or,(x+1)³=i3√3

Or,(x+1)³ +1/(x+1)³ =i3√3+1/i3√3

Or,(x+1)³ +1/(x+1)³ =i26/3√3

When x=1/2-i√3/2

Then, x+1=3/2-i√3/2

Or, (x+1)³=(1/8)(27–i27√3–27+i3√3)

Or,(x+1)³=-i3√3

Or,(x+1)³+1/(x+1)³ =-i3√3+1/-i3√3

Or,(x+1)³+1/(x+1)³ =-i26/3√3

Hence (x+1)³+1/(x+1)³=±i26/3√3