यदि `|(x+a,a^(2),a^(3)),(x+b,b^(2),b^(3)),(x+c,c^(2),c^(3))|=0` तथा a,b,c भिन्न हों तो `x=`

FInd x when det[[x+a,a^(2),a^(3)x+b,b^(2),b^(3)x+c,c^(2),c^(3)]]=0 where a,b,c are distinct numbers and a!=b!=c

Using properties of determinant, find the value of x: |{:(x+a, a^(2), a^(3)), (x+b, b^(2), b^(3)), (x+c, c^(2), c^(3)):}|=0

Solve the system of equations : z+ay+a^(2)x+a^(3)=0z+by+b^(2)x+b^(3)=0z+cy+c^(2)x+c^(3)=0] where a!=b!=c

If ||(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c)|=0 then a,b,c are

If (x-a)^(3)+(x-b)^(3)+(x-c)^(3)-3(x-a)(x-b)(x-c)=0 , then x =

If a, b, c are different, then value of x satisfying the equation |{:( 0 , x^(2) - a , x^(3) - b) , (x^(2) + a , 0 , x^(2) + c), (x^(4) + b , x- c , 0):}|=0 is