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

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

Let x= cos theta and y = sin theta for any real value theta . Then x^(2)+y^(2)=

Find the number of ordered pair of real numbers (x, y) satisfying the equation: 5x(1+1/(x^(2)+y^(2)))=12 & 5y(1-1/(x^(2) + y^(2))) =4

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

Use direct method to evaluate : (viii) (3x^2 + 5y^2) ( 3x^2 - 5y^2)

Find the real numbers (x,y) that satisfy the equation: xy^(2) = 15x^(2) +17xy + 15y^(2) x^(2)y = 20x^(2) + 3y^(2)

If the A.M. and G.M. between two numbers are in the ratio x:y , then prove that the numbers are in the ratio (x+sqrt(x^(2)-y^(2))):(x-sqrt(x^(2)-y^(2))) .

The number of ordered pair(s) (x, y) of real numbers satisfying the equation 1+x^(2)+2x sin(cos^(-1)y)=0 , is :

Solve by matrix method : 2x+y=5 x-y = 1

If x, y, z are positive real numbers such that x+y+z=a, then