`16/n-1=15/(n+1), n!=0,-1` then solve the quadratic equation in `n`

If m and n are the roots of the quadratic equations x^(2) - 3x+1 =0 , then find the value of (m)/( n) + ( n)/(m)

Solve the equation -4+(-1)+2+...+n=437

For what value of n, the equation x^(n)+(1)/(sqrtx)=-k will be a quadratic equation ?

If one root of the quadratic equation ax^2+bx+c=0 is equal to the n^th power of the other root then show that, (ac^n)^(1/(n+1))+(a^nc)^(1/(n+1))+b =0

The value of n for which the equation x^(n)+x^(-n)=k will be a quadratic equation is 1.

If (-1)^(n)+(-1)^(4n)=0 then n is

If one root of the quadratic equation ax^(2) + bx + c = 0 is equal to the n^(th) power of the other root , then show that (ac^(n))^(1/(n+1)) + (a^(n)c)^(1/(n+1))+b = 0

If one root of the quadratic equation ax^(2)+bx+c=0 is equal to the nth power of the other , then show that (ac^n)^((1)/(n+1))+(a^(n)c)^((1)/(n+1))+b=0 .