Question

Quantity-I: Determine the value of (x + y -
z)3 + (x - y +
z)3 - 8x3 . Quantity-II: Determine the value of 6x(z - y -
x) (x - y +
z)

Q: Answer-Quantity-I: Determine the value of (x + y - z)3 + (x - y + z)3 - 8x3 . Quantity-II: Determine the va...

ATQ, Quantity I Given x y - z3 x - y z3- 8x3 Or, x y - z3 x - y z3 -2a3 We know that, a3 b3 c3 3abc, when a b c 0 Here, x y - z a And, x - y z b And, -2x c So, a b c x y - z x - y z - 2x 0 So, required value 3 x y - z x - y z -2x 6xx y - z y - x - z So, Quantity I 6xx y - z y - x - z Quantity II 6xz - y - x x - y z Or, 6x -1 x y - z x - y z Or, 6x -1 -1 x y - z y - x - z So, 6xz - y - x x - y z 6x x y - z y - x - z So, Quantity II 6x x y - z y - x - z So, Quantity I Quantity II

In the question, two Quantities I and II are given. You have to solve both the Quantity to establish the correct relation between Quantity-I and Quantity-II and choose the correct option.

A Quantity I < Quantity II

B Quantity I ≤ Quantity II

C Quantity I ≥ Quantity II

D Quantity I > Quantity II

E Quantity I = Quantity II or No relation can be established