If a = 500, b = 502 and c = 504, then the value of $a^3 + b^3 + c^3 - 3abc$
Answer & explanation
Correct answer: option 3
a3 + b3 + c3 - 3abc = \(\frac{1}{2}\)[(a + b + c) {( a- b)2 + ( b - c)2 + (c - a)2}]
If a = 500
b = 502
c = 504
Then the value of $a^3 + b^3 + c^3 - 3abc$ = \(\frac{1}{2}\) [(500 + 502 + 504) {( 500- 502)2 + ( 502 - 504)2 + (504 - 500)2}]
a3 + b3 + c3 - 3abc = \(\frac{1}{2}\) [(1506) {4+ 4 + 16}]
a3 + b3 + c3 - 3abc = 753 × 24 = 18072