identities

The value of 〖(2-a)〗3+ 〖(2-b)〗3+ 〖(2-c)〗3- 3(2-a)(2-b)(2-c) when a + b + c = 6, is:
3
-3
2
0

2 Answers

206
Sayantan Hazra ·

The question should look like this:

(2 - a)3 + (2 - b)3 + (2 - c)3 - 3(2 - a)(2 - b)(2 - c) = ?

when a + b + c = 6

51
Angikar Ghosal ·

x3 + y3 + z3 − 3xyz = (x + y + z)(x2 + y2 + z2 - xy - yz - xz)

Here x = 2 - a, Here y = 2 - b, Here z = 2 - c

(2 - a)3 + (2 - b)3 + (2 - c)3 - 3(2 - a)(2 - b)(2 - c)
={(2-a) + (2-b) + (2-c)} {(2 - a)2 + (2 - b)2 + (2 - c)2 - (2-a)(2-b) - (2-b)(2-c) - (2-c)(2-a)}
=(2 - a + 2 - b + 2 - c) {(2 - a)2 + (2 - b)2 + (2 - c)2 - (2-a)(2-b) - (2-b)(2-c) - (2-c)(2-a)}
={6 - (a + b + c)} {(2 - a)2 + (2 - b)2 + (2 - c)2 - (2-a)(2-b) - (2-b)(2-c) - (2-c)(2-a)}
=(6 - 6) {(2 - a)2 + (2 - b)2 + (2 - c)2 - (2-a)(2-b) - (2-b)(2-c) - (2-c)(2-a)}
=0 * {(2 - a)2 + (2 - b)2 + (2 - c)2 - (2-a)(2-b) - (2-b)(2-c) - (2-c)(2-a)}
=0

Answer) 0, zero, nada, nil, null, nothing

Your Answer

Close [X]