" (a) "[(3)/(2)x+1]^(3)quad " (m) "[x-(2)/(3)y]

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)

If the two lines (x-1)/(-3) = (y-2)/(2m) = (z-3)/2 and (x-1)/(3m) = (y-5)/1 = (z-6)/(-5) are mutually perpendicular , then : m

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 + y + z = xyz , prove that (3x -x^(3))/ (1-3x^(2)) + (3y -y^(3))/(1- 3y^(2)) +(3z -z^(3))/(1- 3z^(2)) = (3x -x^(3))/(1-3x)^(2) * (3y- y^(3))/(1-3x)^(2)* (3z- z^(3))/(1-3z)^(2) .

If y = 2x + 3x ^ (2) + 4x ^ (3) + ......., then (y) / (2) - (1.3) / (2!) ((Y) / (2) ) ^ (2) + (1.3.5) / (3!) ((Y) / (3)) ^ (3) -...... oo =

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

"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)

The value of ,2x_(1)y_(1),x_(1)y_(2)+x_(2)y_(1),x_(1)y_(3)+x_(3)y_(1)x_(1)y_(2)+x_(2)y_(1),2x_(2)y_(2),x_(2)y_(3)+x_(3)y_(2)x_(1)y_(3)+x_(3)y_(1),x_(2)y_(3)+x_(3)y_(2),2x_(3)y_(3)]| is