⭐ Olympiad Mathematics Question With Solution
📌 Question
If
x + 1/x = 3
x^3 + 1/x^3 = 18
✔ Solution (Step-by-Step Explanation)
We know the identity:
Given:
x + 1/x = 3
Cube both sides:
(x + 1/x)^3 = 3^3
Using identity:
(x + 1/x)^3 = x^3 + 1/x^3 + 3(x + 1/x)
Substitute the value:
27 = x^3 + 1/x^3 + 3(3)
27 = x^3 + 1/x^3 + 9
Therefore:
x^3 + 1/x^3 = 18
⭐ Final Answer
x^3 + 1/x^3 = 18
🔥 Why this is an important Olympiad trick?
This question teaches how to solve cube identities without directly expanding powers.
Such tricks save time in:
-
Math Olympiad
-
NTSE
-
JEE / NEET
-
School competitive tests
📝 Try Yourself (Bonus Practice)
If
x + 1/x = 4
Find:
x^3 +1/x^3 = ?
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