" c) If "a+2b=5;" then show that: "a^(3)+8b^(3)+30ab=125

If a + 2b + c= 0 , then show that: a^(3) + 8b^(3) + c^(3)= 6abc

If c^(2) ne ab and the roots of (c^(2)-ab)x^(2)-2(a^(2)-bc)x+(b^(2)-ac)=0 are equal, then show that a^(3)+b^(3)+c^(3)=3abc" or "a=0

If a,b,c are in A.P,show that (i)a^(3)+b^(3)+6abc=8b^(3)( ii) (a+2b-c)(2b+c-a)(a+c-b)=4abc

If 3a + 5b + 4c= 0 , show that: 27a^(3) + 125b^(3) + 64 c^(3) = 180 abc

If 2^(a)=3^(b)=6^(c) then show that c=(ab)/(a+b)

If a + b +5 = 0 , then find the value (a^(3)+b^(3)-15ab+125)

If a + b + c = 0 , show that a^(3) + b^(3) + c^(3) = 3abc The following are the steps involved in showing the above result. Arrange them in sequential order (A) a^(3) + b^(3) + 3ab (-c) = -c^(3) (B) (a + b)^(3) = (-c)^(3) (C) a + b + c = 0 rArr a + b = -c (D) a^(3) + b^(3) + 3ab (a +b) = -c^(3) (E) a^(3) + b^(3) + c^(2) = 3abc

If a, b, c and d are in proportion, then show that (a^(3)+3ab^(2))/(3a^(2)b+b^(3))=(c^(3)+3cd^(2))/(3c^(2)d+d^(3))

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

If a, b, c are in A.P, show that (i)a^3+b^3+6abc=8b^3 (ii) (a+2b-c)(2b+c-a)(a+c-b) =4abc