By using properties of determinants. Show that: (i) `|x+4 2x2x2xx+4 2x2x2xx+4|=(5x-4)(4-x)^2` (ii) `|y+k y y y y+k y y y y+k|=k^2(2ydotk)^2`

By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2 (ii) |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)

By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2 (ii) |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)

Using properties of determinants, prove the following |[x,x+y,x+2y],[x+2y,x,x+y],[x+y,x+2y,x]|=9y^2(x+y)

Show that (x^2+y^2)^4=(x^4-6x^2y^2+y^4)^2+(4x^3y-4x y^3)^2dot

Show that (x^2+y^2)^4=(x^4-6x^2y^2+y^4)^2+(4x^3y-4x y^3)^2dot

Factorize: x^4+2x^2y^2+y^4

Given that x^2 + y^2 =4 and x^2 + y^2 -4x -4y =-4 , then x + y =

Divide: (i) x+2x^2+3x^4-x^5\ by 2x , (ii) y^4-3y^3+1/2y^2\ by 3y

Three sides of a triangle are represented by lines whose combined equation is (2x+y-4) (xy-4x-2y+8) = 0 , then the equation of its circumcircle will be : (A) x^2 + y^2 - 2x - 4y = 0 (B) x^2 + y^2 + 2x + 4y = 0 (C) x^2 + y^2 - 2x + 4y = 0 (D) x^2 + y^2 + 2x - 4y = 0

If (4x+3y)/(4x-3y)=7/4 use the properties to find the value of (2x^2-11y^2)/(2x^2+11y^2)