Sets, Relations & Functions
Functions
star_batch_jee_advanced_2025
Grade 11
Question:
The number of positive integers $x$ that satisfy $3^x = x^3 + 3x^2 + 2x + 1$ is:
Step-by-Step Solution
Key Concept: Modular arithmetic can eliminate solutions by comparing residues on both sides of an equation.
We have $3^x = x(x+1)(x+2) + 1$. The LHS is a multiple of 3 while the RHS is not divisible by 3, creating a contradiction.
Correct Answer: 1