Question

2x – 5y = 7z-3y then, for xyz ≠ 0, (8x3 -343z3 -8y3 ) / xyz =?

Answer 1

Answer:

Step-by-step explanation:

Given :

To find the value of, $\frac{8x^3 - 343z^3 - 8y^3}{xyz}$,

if 2x - 5y = 7z - 3y,.

Solution :

We know that,

a³ + b³ + c³ - 3abc = 0 , ...(i)

if  a + b + c = 0,.

So,

by solving the given equation,

We get,

2x - 5y = 7z - 3y

2x - 5y + 3y - 7z = 0

⇒ 2x - 2y - 7z = 0,.   ...(ii)

Let a = 2x , b = - 2y , c = - 7z,

Then,

a + b + c - 0,.  

Hence,

a³ + b³ + c³ - 3abc = 0

⇒ a³ + b³ + c³ = 3abc

⇒ (2x)³ + (- 7y)³ + (- 2y)³ = 3(2x)(-7y)(-2z)

⇒ 8x³ - 343y³ - 8z³ = 84xyz

⇒ $\frac{8x^3 - 343y^3 - 8z^3}{xyz} = 84$