य‌द‌ि `(x-a^(2))/(b+c)+(x-b^(2))/(c+a)+(x-c^(2))/(a+b)=4(a+b+c)`, then `x` ‌ किसके बराबर है ?

Factorise : x^(2)(b-c)+b^(2)(c-x)+c^(2)(x-b)

ab(a-b)+bc(b-c)+ca(c-a) is equal to : ab(a-b)+bc(b-c)+ca(c-a) किसके बराबर है ?

If (x)/((b-c)(b+c-2a))=(y)/((c-a)(c+a-2b))=(z)/((a-b)(a+b-2c)) then the value of (x+y+z) is :

Prove that (x-a)^2/((a-b)(a-c))+(x-b)^2/((b-a)(b-c))+(x-c)^2/((c-a)(c-b))=1

(a^2/(x-a)+b^2/(x-b)+c^2/(x-c)+a+b+c)/(a/(x-a)+b/(x-b)+c/(x-c))

If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))| = (a - b) (b - c) (c - a) (a + b + c) , where a,b,c are all different, then the determinant |(1,1,1),((x-a)^(2),(x-b)^(2),(x-c)^(2)),((x-b)(x-c),(x-c)(x-a),(x-a)(x-b))| vanishes when a)a + b + c = 0 b) x = (1)/(3) (a + b + c) c) x = (1)/(2) (a + b + c) d) x = a + b + c