If `x, y` are rational numbers such that `x+ y+(x-2y)sqrt2=2x-y+(x-y-1)sqrt6` then

If x, y are rational numbers such that (x+y)+(x-2y)sqrt(2)=2x-y+(x-y-1)sqrt(5) then

If x, y are rational numbers such that (x+y)+(x-2y)sqrt(2)=2x-y+(x-y-1)sqrt(5) then

If x and y are real numbers such that (x+sqrt(1+x^(2)))(y+sqrt(1+y^(2)))=1. Then find x+y

If x and y are rational and if x (3 + 2 sqrt2) - y sqrt2 = y(5 -3 sqrt2) + 7(2 + x sqrt2) , then find the value of x and y

(sqrt(x)+sqrt(y))^(2)=x+y+2sqrt(xy) and sqrt(x)sqrt(y)=sqrt(xy) , where x and y are positive real numbers . If x=2sqrt(5)+sqrt(3) and y=2sqrt(5)-sqrt(3) , then x^(4)+y^(4) =

(sqrt(x)+sqrt(y))^(2)=x+y+2sqrt(xy) and sqrt(x)sqrt(y)=sqrt(xy) , where x and y are positive real numbers . If a=1+sqrt(2)+sqrt(3) and b=1+sqrt(2)-sqrt(3) , then a^(2)+b^(2)-2a-2b=

If x>y prove that sqrt(y+sqrt(2xy-x^2))+sqrt(y-sqrt(2xy-x^2)) = sqrt(2x) .