Suppose `xa n dy` are real numbers and that `x^2+9y^2-4x+6y+4=0` . Then the maximum value of `((4x-9y))/2` is__________

Let xa n dy be two real variable such that x >0a n dx y=1 . Find the minimum value of x+y .

For any x,y, in R,xygt0 . Then the minimum value of (2x)/(y^3)+(x^3y)/(3)+(4y^2)/(9x^4) is ___________.

If xa n dy are real numbers such that 2log(2y-3x)=logx+logy ,then find x/y .

Let P(x)=5/3-6x-9x^2a n dQ(y)=-4y^2+4y+(13)/2dot if there exists unique pair of real numbers (x , y) such that P(x)Q(y)=20 , then the value of (6x+10 y) is _____.

The circle x^2 + y^2 - 4x + 6y + c = 0 touches x axis if

Find the values of the real numbers x and y if 3x + (2x - 3y) i=6 + 3i^(9)

Prove that for all real values of xa n dy ,x^2+2x y+3y^2-6x-2ygeq-11.

If m is the minimum value of f(x , y)=x^2-4x+y^2+6y when xa n dy are subjected to the restrictions 0lt=xlt=1a n d0lt=ylt=1, then the value of |m| is________

Given that x ,y ,z are positive real such that x y z=32. If the minimum value of x^2+4x y+4y^2+2z^2 is equal m , then the value of m//16 is.