Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
Let $x, y, z$ be non-zero real numbers such that $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}=7$ and $\frac{y}{x}+\frac{z}{y}+\frac{x}{z}=9$, then $\frac{x^{3}}{y^{3}}+\frac{y^{3}}{z^{3}}+\frac{z^{3}}{x^{3}}-3$ is equal to
MathematicsBasic of MathematicsKVPYKVPY 2013 (SA)
Options:
  • A $152$
  • B $153$
  • C $154$
  • D $155$
Solution:
1115 Upvotes Verified Answer
The correct answer is: $154$
$a^{3}+b^{3}+c^{3}-3 a b c=[a+b+c]\left[(a+b+c)^{2}-3(a b+b c+c a)\right]$
$=[7]\left[(7)^{2}-3(9)\right]$
$=7(49-27)=7 \times 22=154$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.