If 8x3 + 27y3 + 64z3 = 72 xyz, then the relation between x, y and z can be:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 2x + 3y = −4z
Concept used:
If x3 + y3 + z3 = 3xyz then
x + y + z = 0
Calculations:
⇒ 8x3 + 27y3 + 64z3 = 72 xyz
Using the above concept;
⇒ (2x)3 + (3y)3 + (4z)3 = 3 × (2x)(3y)(4z)
Hence, 2x + 3y + 4z = 0
Therefore, 2x + 3y = -4z