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

Find the values of xa n dy if [x+10 y^2+2y0-4]=[3x+4 3 0y^2-5y]

Prove by direct method that for any real number x,y if x = y then x^(2) = y^(2) .

Prove that the centres of the circles x^(2)+y^(2)=1,x^(2)+y^(2)+6x-2y-1=0 and x^(2)+y^(2)-12x+4y=1 are collinear

If the equation x^(2)+9y^(2)-4x+3=0 is satisfied for all real values of x and y, then

Prove that sin^(2)theta=((x+y)^(2))/(4)xy is possible for real values of x and y only when x=y and x!=0.

Find the angle of intersection of the following curves : y^2=xa n dx^2=y y=x^2a n dx^2+y^2=20 2y^2=x^3a n dy^2=32 x x^2+y^2-4x-1=0a n dx^2+y^2-2y-9=0 (x^2)/(a^2)+(y^2)/(b^2)=1a n dx^2+y^2=a b x^2+4y^2=8a n dx^2-2y^2=2 x^2=27ya n dy^2=8x x^2+y^2=2xa n dy^2=x y=4-x^2a n dy=x^2

Let ' n ' is the number of ordered pair (x ,y) satisfying the system of equations {x^2y^2-2x+y^2=0 2x^2-4x+3+y^2=0(x , y in R) and ' S ' is the sum of all the values of xa n dy satisfying the given system of equations then n > S (b) n

Find the greatest and the least real value of x$ y satisfy the relation x^(2)+y^(2)=6x-8y

Find the greatest and least value of y= x^(3)-3x^(2) + 6x-2 on [-1,1] y is differentiable function of x and y'(x) = 3x^(2) -6x + 6= 3(x^(2) -2x+2) =3(x-1)^(2) gt 0 .

Let y=sqrt(2/(x^(2)-x+1)-1/(x+1)-(2x+1)/(x^(3)+1)) , find all the real values of x for which y takes real values.