Notifications
Clear all
Polynomials
1
Posts
2
Users
0
Likes
626
Views
0
07/07/2021 11:07 am
Topic starter
Without actually calculating the cubes, find the value of each of the following:
(i) (−12)3 + (7)3 + (5)3
(ii) (28)3 + (−15)3 + (−13)3
1 Answer
0
07/07/2021 11:09 am
(i) (−12)3+(7)3+(5)3
Let a = -12
b = 7
c = 5
We know that if x + y + z = 0, then x3+y3+z3=3xyz.
Here, −12 + 7 + 5 = 0
(−12)3+(7)3+(5)3 = 3xyz
= 3 × -12 × 7 × 5
= -1260
(ii) (28)3+(−15)3+(−13)3
(28)3+(−15)3+(−13)3
Let a = 28
b = −15
c = −13
We know that if x + y + z = 0, then x3+y3+z3 = 3xyz.
Here, x + y + z = 28 – 15 – 13 = 0
(28)3+(−15)3+(−13)3 = 3xyz
= 0 + 3(28)(−15)(−13)
= 16380