By using properties of determinants, prove that,
`|{:(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4):}|=(5x+4)(x-4)^(2)`

By using properties of determinats. Prove that- |(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)

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 )

Solve : |(x+4, 2x,2x),(2x , x+4, 2x),(2x, 2x, x+4)| = 0

|{:(x+y,x,x),(5x+4y,4x,2x),(10x+8y,8x,3x):}|=x^3

|{:(x," "4,-2),(4," "x,-2),(4,-2," "x):}|=0

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

|{:(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,3x-64):}|=0

Using the properties of proportion, solve for x, given (x^4+1)/(2x^2)=17/8 .

If a,b,c are in A.P. then the determinant {:|( x+2,x+3,x+2a),( x+3,x+4,x+2b),( x+4,x+5,x+2c)|:} is