" (話) "[(x)/(2)+(y)/(3)=1],[(x)/(3)+(y)/(2)=1]

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)

Find the following products and verify the result for x=-1,y=-2:(3x-5y)(x+y)(2)(x^(2)y-1)(3-2x^(2)y)((1)/(3)x-(y^(2))/(5))((1)/(3)x+(y^(2))/(5))

If A(x_(1), y_(1)), B(x_(2), y_(2)) , and, C(x_(3), y_(3)) are vertices of an equilateral triangle whose each side is equal to a, then prove that |(x_(1), y_(1), 2),(x_(2), y_(2), 2),(x_(3), y_(3), 2)|^(2) = 3a^(4) .

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

"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 (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) ))