If `(x_i ,y_i),i=1,2,3,` 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 find the value of `(x_1+x_2+x_3)/(y_1+y_2+y_3)` .

If (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are vertices of 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

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) ))

If (x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2)) and (x_(3),y_(3),z_(3)) are the vertices of an equilateral triangle such that (x_(1)-2)^(2)+(y_(1)-3)^(2)+(z_(1)-4)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)+(z_(2)-4)^(2) =(x_(3)-2)^(2)+(y_(3)-3)^(2)+(z_(3)-4)^(2) then sum x_(1)+2sum y_(1)+3sum z_(1)

If ((2x-y)/(x+2y))=(1)/(2), then find the value of ((3x-y)/(3x+y))

if x=1/(√3+√2) and y=1/(√3-√2) . then find the value of x+y and x-y

If the co-ordinates of the vertices of an equilateral triangle with sides of length a are (x_1,y_1), (x_2, y_2), (x_3, y_3), then |[x_1,y_1,1],[x_2,y_2,1],[x_3,y_3,1]|=(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

An equilateral triangle has each side equal to a,If (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are the vertices of the triangle then det[[x_(1),y_(1),1x_(2),y_(2),1x_(3),y_(3),1]]^(2)=

An equilateral triangle has each side equal to a,If (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are the vertices of the triangle then det[[x_(1),y_(1),1x_(2),y_(2),1x_(3),y_(3),1]]^(2)=