If p + q + r = 0, then what is the value of (p + q - r) ^3 + (r + p - q) ^3 + (q + r - p) ^3 ?

Algebra and Applications Test 3

Question : 23 of 25

Marks: +1, -0

p + q + r = 0

, then what is the value of

(p + q - r) ^3

+ (r + p - q) ^3

+ (q + r - p) ^3

Solution:

∵ p+q-r+r+p-q+q+r-p

=p+q+r=0

(∵p + q + r = 0)

(p + q - r) ^3 + (r + p - q) ^3 + (q + r - p) ^3

=3(p + q - r) (r + p - q) (q + r - p)

=3(-r - r) (-q - q) (-p - p)

(∵p + q + r = 0)

=3(-2r ) (-2q ) (-2p ) =-24pqr

Go to Question:

Prev Question

Next Question