Prove that if the equation `x^2+9y^2-4x+3=0` is satisfied for real values of `xa n dy ,t h e nx` must lie between 1 and 3 and`y` must lie between-1/3 and 1/3.

If x^2 + 4y ^2 - 8x +12 =0 is satified by real values of x nad y then y must lies between

Find the real values of xa n dy , if (3x-7)+2i y=-5y+(5+x)i

The real number k for which the equation, 2x^3+""3x""+""k""=""0 has two distinct real roots in [0, 1] (1) lies between 2 and 3 (2) lies between -1 and 0 (3) does not exist (4) lies between 1 and 2

The real number k for which the equation, 2x^3+""3x""+""k""=""0 has two distinct real roots in [0, 1] (1) lies between 2 and 3 (2) lies between -1 and 0 (3) does not exist (4) lies between 1 and 2

Number of integral value (s) of k for which the equation 4x^(2)-16x+k=0 has one root lie between 1 and 2 and other root lies between 2 and 3, is

For what real values of k both the roots of equation x^2+2(k-3)x+9=-0 lie between -6 and 1.

If f(x , y) satisfies the equation 1+4x-x^2=sqrt(9sec^2y+4cos e c^2y) then find the value of xa n dtan^2ydot

Find the real values of x and y satisfying the equality (x-2 + (y-3)i)/(1+i)= 1-3t

If t is a real number satisfying the equation 2t^3-9t^2+30-a=0, then find the values of the parameter a for which the equation x+1/x=t gives six real and distinct values of x .

If x is real, prove that the value of the expression ((x-1)(x+3))/((x-2)(x+4)) cannot be between (4)/(9) and 1.