Question

if x+1/x =5 then the sum of digits of x^9+ 1/x^9 is​

Answer 1

Answer:

x-(1/x) = 2

By LCM we get

x^2 -2x-1=0. It is quadratic equation.hence

x = {2+√(4+4)}/2 and {2-√(4+4)}/2

x = 1+√2 and 1-√2

Substitute ‘x = 1+√2’ in the x^9 -(1/x^9)

= (1+√2 )^9 -1/((1+√2 )^9)

= 2786

Substitute ‘x = 1-√2’ in the x^9 -(1/x^9)

= (1-√2 )^9 -1/((1-√2 )^9)

= 2786

Hence the value of x^9 - 1/x^9 = 2786