If `y=(x^(2//3)-x^(-1//3))/(x^(2//3)+x^(-1//3))," then "(x+1)^(2)y_(1)=`

Evaluate : (x^(1//3)+y^(1//3))(x^(2//3)-x^(1//3)y^(1//3)+y^(2//3)) , when x=4(5)/(7) " and " y=5(2)/(7) .

if (x_ (1), y_ (1)), (x_ (2), y_ (2)), (x_ (3), y_ (3)) are vertices equilateral triangle such that (x_ (1) -2) ^ (2) + (y_ (1) -3) ^ (2) = (x_ (2) -2) ^ (2) + (y_ (2) -3) ^ (2) = (x_ (3) - 2) ^ (2) + (y_ (3) -3) ^ (2) then x_ (1) + x_ (2) + x_ (3) +2 (y_ (1) + y_ (2) + y_ (3) ))

Find the value of (x+y) ,if (x+(y^(3))/(x^(2)))^(-1)-((x^(2))/(y)+(y^(2))/(x))^(-1)+((x^(3))/(y^(2))+y)^(-1)=(1)/(3)

"Find the value of "(x+y)," if "(x+(y^(3))/(x^(2)))^(-1)-((x^(2))/(y)+(y^(2))/(x))^(-1)+((x^(3))/(y^(2))+y)^(-1)=(1)/(3)

If (x_(1), y_(1)), (x_(2), y_(2)), (x_(3), y_(3)) are the vertices of an equilateral triangle such that (x_(1)-2)^(2)+(y_(1)-3)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)=(x_(3)-2)^(2)+(y_(3)-3)^(2) then x_(1)+x_(2)+x_(3)+2(y_(1)+y_(2)+y_(3))=

If the coordinates of the vertices of an equilateral triangle with sides of length a are (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) then |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2=(3a^(4))/4

If the coordinates of the vertices of an equilateral triangle with sides of length a are (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) then |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2=(3a^(4))/4