Without actually cal.culating the cubes, find the value of each of the following: (i) (- 12'1 + <7'1 +

(i) Consider (- 12>3 + (7>3 + (5>3 Let z = - 12, y = 7, z = 5 Now, x + y + z = -:- 12 + 7 + 6 = 0 We know, if x + y + z = 0, then x3 + y3 + z3 = 3%yz. / :. <- 12>3 + (7>3 + (6)3 • 3(- 12X7X5) = - 21 x 60 = - 1260. 44 (ii) Consider (28)' + (- 15>3 + (- 13)3 Let :t = 28, y = - 15, z = - 13 Now, x + y + z = 28 - 15 - 13 = 0 We know, if x + y + z = 0, then + y3 + :r:3 = :h:yz. ... (28)3 + (- 15>3 + (- 13>3 = 3(28)(- 16X- 13) = 16380.