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Solve for x in the equation x^x + 6/x = 7
Published on November 5, 2024
Algebra
The equation x^x + 6/x = 7 has two solutions, x = 1 and x = 2, as demonstrated by direct substitution.
Question
\( x^{x}+\frac{6}{x}=7 \)
Answer
We are asked to solve the equation
Let
If
So
So
If
So
So
If
Since
Let’s consider the case when
If
If
Since
Let’s consider the case when
If
If
Consider the derivative of
Differentiating both sides with respect to
Differentiating both sides with respect to
So
If
If
If
If
Final Answer: The final answer is