`|[x+4,2x,2x] , [2x,x+4,2x] , [2x,2x,x+4]|=(5x+4)(x-4)^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)

If |(x-4,2x,2x),(2x,x-4,2x),(2x,2x,x-4)|=(A+Bx)(x-A)^2 then the ordered pair (A,B) is equal to

By using properties of determinants,prove the following ,2xdet[[x+4,2x,2x2x,x+4,2x2x,2x,x+4]]=(5x+4)(4-x)^(2)

det [[x + 4,2x, 2x2x, x + 4,2x2x, 2x, x + 4]]

(3x + 2x^2 + 4x^3) / (x-4)

(3x+4)(2x-3)+(5x-4)(x+2)

(5-2x) (3x + 4) (x-4)> = 0

If |[2,4],[5,1]|=|[2x,4],[6,x]| then x is

2x^2(x^3-x)-3x(x^4+2x)-2(x^2-3x^4)