If the roots of the equation `(c^2-a b)x^2-2(a^2-b c)x+b^2-a c=0` are equal, prove that either `a=0` or `a^3+b^3+c^3=3a b cdot`

If the roots of the equation (c^2-a b)x^2-2(a^2-b c)x+b^2-a c=0 are equal, prove that either a=0 or a^3+b^3+c^3=3a b c dot

If the roots of the equation (c^(2)-ab)x^(2)-2(a^(2)-bc)x+b^(2)-ac=0 are equal,prove that either a=0 or a^(3)+b^(3)+c^(3)=3abc

If the roots of the equation (c^(2)-ab)x^(2)-2(a^(2)-bc)x+b^(2)-ac=0 in x are equal, show that either a=0 or a^(3)+b^(3)+c^(3)=3abc .

If the roots of the equation (c^(2)-ab)x^(3)-2(a^(2)-bc)x+b^(2)-ac=0 are real and equal prove that either a=0 (or) a^(3)+b^(3)+c^(3)=3"abc" .

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c .

If the roots of the equation (b-c)x^(2)+(c-a)x+(a-b)=0 are equal,then prove that 2b=a+c

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c

If the roots of the equation x^2-2(a+b)x+a(a+2b+c)=0 be equal , prove that a,b, c are in G.P,

Show that the roots of the equation (a^2-bc)x^2+2(b^2-ca)x+c^2-ab=0 are equal if either b=0 or , a^3+b^3+c^3-3abc=0

If the roots of the equations (b-c) x^(2) + (c-a) x+( a-b) =0 are equal , then prove that 2b=a+c