Question

If the value of a${}^3$+b${}^3$+c${}^3$-3abc = 10k, then find the value of k, when a = 249, b = 250 and c = 251.

• A. 225
• B. 2250
• C. 250
• D. 2500
• E. None of these

Answer 1

The correct option is A

225

a${}^3$+b${}^3$+c${}^3$-3abc = 0.5(a+b+c)[(a-b)${}^2$​ + (b-c)${}^2$​ + (c-a)${}^2$​] = 0.5 x 750 x 6 = 2250

Now, 10k = 2250 $⟹$ k = 225