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

One of the two real roots of the quadratic equation ax^(2)+bx+c=0 is three times the other. Then prove that b^(2)-4ac=(4ac)/(3)

Prove that ((n+1)/(2))^(n) gt (n!)

If one root of the equation bx^2+mx+n=0 is 9/2 and m/(4n)=l/m , then l+n is equal to

Prove that cos^(-1)((1-x^(2n))/(1+x^(2n)))=2 tan^(-1)x^n

Prove that ""^(n+1)C_(r+1)=(n+1)/(r+1)"^nC_r

If alpha and beta are the roots of the equation ax^(2) + bx + c = 0, (c ne 0) , then the equation whose roots are (1)/(a alpha +b) and (1)/(a beta + b) is

If alpha, beta are the roots of ax^(2)+2bx+c=0 and alpha +delta, beta + delta are those of Ax^(2)+2Bx+C=0 , then prove that (b^(2)-ac)/(B^(2)-AC)= ((a)/(A))^(2)