Number of solutions of $2^{x} + 3^{x} + 4^{x} = 5^{x}$ is

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Solution

we know that,
$3^{2} + 4^{2} = 5^{2}$ (Pythagorean triplet)

So, there is no such value of $x$ such that, $2^{x} + 3^{x} + 4^{x} = 5^{x}$

Number of solutions $= 0$

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