Prove that for real values of `x ,(a x^2+3x-4)//(3x-4x^2+a)` may have any value provided a lies between 1 and 7.

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.

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.

Find the maximum value of (7−x)^4 (2+x)^5 when x lies between −2 and 7.

Prove that the values of the function (sinxcos3x)/(sin3xcosx) cannot lie between 1/3 and 3 for any real x

Find the real values of x and y, if (3x - 7) + 2 iy = -5y + (5 + x)i

If x=7+4sqrt3 then find the value of x+(1)/(x)

For all real values of x, the minimum value of (1-x+x^(2))/(1+x+x^(2)) is

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

The set of all values of x for which ((x+1)(x-3)^(2)(x-5)(x-4)^(3)(x-2))/(x) lt 0

Find all real values of x which satisfy x^2-3x+2>0a n dx^2-2x-4lt=0.