If x + 1/x = -2 , then the value of x 2n-1 + 1/ x2n+1 where n is a - Maths - Exponents and Powers

Question

If x + 1/x = -2 , then the value of x 2n-1 + 1/
x2n +1 where n is a positive integer , is

Rajat Sethi · Accepted Answer

Given,x+1x=-2It is only possible when x=-1,i,e -1+1-1=-2Now,x2n+1+1x2n+1=x2n
x+1x2n
x=(-1)2n(-1)+1(-1)2n(-1)Since,n is a positive integer,So, even power of n will be positivex2n+1+1x2n+1=(1)(-1)+1(1)(-1)=-1+1-1=-2

If x + 1/x = -2 , then the value of x 2n-1 + 1/ x2n +1 where n is a positive integer , is

If x + 1/x = -2 , then the value of x ^2n-1 + 1/ x²ⁿ ^{+1 where n is a positive integer , is}