If a=c, show that cba-abc=0

If c gt a , show that cba-abc=99(c-a)

If a = b, show that abc = bac.

if a gt c , show that abc - cba = 99(a - c)

If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]| =0, show that abc(ab+bc+ac) = a+b+c

If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]| =0, show that abc(ab+bc+ac) = a+b+c

If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]| =0, show that abc(ab+bc+ac) = a+b+c

If a,b,c in R and equations ax^2 + bx + c = 0 and x^2 + 2x + 9 = 0 have a common root, show that a:b:c=1 : 2 : 9.

If a=log_(24)12,b=log_(36)24, c=log_(48)36 , then show that 1+abc=2bc

If a+ b + c = 0 , show that : a^(3) + b^(3) + c^(3)= 3abc

If equations ax^(2)-bx+c=0 (where a,b,c epsilonR and a!=0 ) and x^(2)+2x+3=0 have a common root, then show that a:b:c=1:2:3