[" 38.Using proportion determinants prove that "],[qquad |[1,x,x+1],[2x,x(2x-1),x(x+1)],[3x(1-x),x(x-1)(x-2),x(x+1)(x-1)]|=6x^(2)(1-x^(2))]

prove that |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(1-x),x(x-1)(x-2),x(x+1)(x-1))|=6x^(2)(1-x^(2))

Using the properties of determinants, prove that following : |{:(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(1-x),x(x-1)(x-2),x(x+1)(x-1)):}|=6x^(2)(1-x^(2))

If f(x)=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)):}| then

Using properties of determinants, prove the following: |[1,x,x^2],[x^2, 1,x],[x,x^2,1]|=(1-x^3)^2

Using properties of determinants, prove the following: |[1,x,x^2],[x^2, 1,x],[x,x^2,1]|=(1-x^3)^2

By using properties of determinants. Show that: |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=(1-x^3)^2

By using properties of determinants, show that : |[1,x,x^2],[x^2,1,x],[x,x^2,1]| = (1-x^3)^2

Using properties of determinants prove the following. abs[[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2