[" If "(1)/(2)+(2)/(y)=4" and "(3)/(y)-(1)/(x)=11" then "],[qquad [x=-2,y=3],[x=(-1)/(2),y=(1)/(3)],[x=(-1)/(2),y=3],[x=2,y=3]]

If (1)/(x) + ( 2)/(y) = 4 and ( 3)/(y) - (1)/(x) = 11 then

(x) / (2) + (y) / (3) = 1 (x) / (3) + (y) / (2) = 1

3x+y=1,2x=11y+3

If (x_(1)-x_(2))^(2)+(y_(1)-y_(2))^(2)=144,(x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=25 and (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=169, then the value of det[[x_(1),y_(1),1x_(2),y_(2),1x_(3),y_(3),1]]^(2) is 30(b)30^(2)(c)60(d)60^(2)

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

Find each of the following products: (i) (x - 4)(x - 4) (ii) (2x - 3y)(2x - 3y) (iii) ((3)/(4) x - (5)/(6) y) ((3)/(4)x - (5)/(6) y) (iv) (x - (3)/(x)) (x - (3)/(x)) (v) ((1)/(3) x^(2) - 9) ((1)/(3) x^(2) - 9) (vi) ((1)/(2) y^(2) - (1)/(3) y) ((1)/(2) y^(2) - (1)/(3) y)