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Question

find the number of solution of the equation 3^x+4^x=5^x
 


Solution

3^x+4^x-5^x=0

For x<=1, value is positive.
For x>=3, value is negative.
So the value of x lies in between 1 and 3.
The only number satisfying the equation is 2. So number of solution is 1.

OR

divide directly by 5^x and get 1=(3/5)^x+(4/5)^x1. From here it is clear that the RHS is strictly decreasing, and there is a unique solution

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