Show that a real value of `x` will satisfy the equation `(1-i x)//(1+i x)=a-i b` if `a^2+b^2=1,w h e r ea ,b` real.

The sum of all real values of X satisfying the equation (x^2-5x+5)^(x^2 + 4x -60) = 1 is:

Solve the equation |a-x c b c b-x a b a c-x|=0w h e r ea+b+c!=0.

The number of real root of the equation e^(x-1)+x-2=0 , is

Number of real values of x satisfying the equation log_2(x^2-x)*log_2((x-1)/x)+(log_2x)^2=4 ,is (a) 0 (b) 2 (c) 3 (d) 7

The number of real values of x satisfying tan^-1(x/(1-x^2))+tan^-1 (1/x^3) = (3 pi)/4 is

If the sum of square of roots of the equation x^2+(p+i q)x+3i=0 is 8, then find the value of pa n dq j ,w h e r epa n dq are real.

If a, b are real then show that the roots of the equation (a-b)x^(2)-6(a+b)x-9(a-b)=0 are real and unequal.

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0w h e r ea ,b ,c in Rdot

Solve the equation x^2-x+1=1/2+sqrt(x-3/4),w h e r exgeq3/4dot

Consider a real-valued function f(x) satisfying 2f(x y)=(f(x))^y+(f(y))^xAAx , y in Ra n df(1)=a ,w h e r ea!=1. Prove that (a-1) sum_(i=1)^nf(i)=a^(n+1)-a