If `((1)/(2))^(y)=(1)/(4)xx2^(y)`, what is y?

If x=1+(y)/(2)+((y)/(2))^(2)+((y)/(2))^(3)+……" where "|y|lt2 , what is 1y equal to ?

If (1)/(x) + (1)/(y) = 2 and (3)/(x) + (4)/(y) = 7 , what is the value of (x + y) ?

The solution of (dy)/(dx)=(1)/(2x-y^(2)) is given by , (A) y=Ce^(-2x)+(1)/(4)x^(2)+(1)/(2)x+(1)/(4)," 4"(1)/(2)," (B) "x=Ce^(-y)+(1)/(4)y^(2)+(1)/(4)y+(1)/(2)," (C) "x=Ce^(y)+(1)/(4)y^(2)+y+(1)/(2)," (D) "x=Ce^(2y)+(1)/(2)y^(2)+(1)/(2)y+(1)/(4)

If (x - ( 1)/( 3))^(2) + ( y - 4)^(2) = 0 , then what is the value of ( y +x)/( y -x) ?

[" The solution of "(dy)/(dx)=(1)/(2x-y^(2))" is given by "],[[" (A) "y=Ce^(-2x)+(1)/(4)x^(2)+(1)/(2)x+(1)/(4)," (B) "x=Ce^(-y)+(1)/(4)y^(2)+(1)/(4)y+(1)/(2)],[" (C) "x=Ce^(y)+(1)/(4)y^(2)+y+(1)/(2)," (D) "x=Ce^(2y)+(1)/(2)y^(2)+(1)/(2)y+(1)/(4)]]

((a^(x^(2)))/a^(y^(2)))^((1)/(x+y))xx((a^(y^(2)))/a^(z^(2)))^((1)/(y+z))xx((a^(Z^(2)))/a^(x^(2)))^((1)/(z+x))= _______