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Question Number 207673 by efronzo1 last updated on 22/May/24

$$\underset{―}{}$$$$$$

Answered by A5T last updated on 22/May/24

$$abcde=a+b+c+d+e⩽5e\Rightarrow abcd⩽5$$$$abcd=1\Rightarrow a=b=c=d=1$$$$\Rightarrow a+b+c+d+e=4+e=eX$$$$abcd=2\Rightarrow a=b=c=1;d=2$$$$\Rightarrow a+b+c+d+e=5+e=2e\Rightarrow e=5$$$$abcd=3\Rightarrow a=b=c=1;d=3$$$$\Rightarrow a+b+c+d+e=6+e=3e\Rightarrow e=3$$$$abcd=4\Rightarrow \left(i\right):a=b=c=1;d=4$$$$\Rightarrow a+b+c+d+e=7+e=4eX$$$$\left(ii\right):a=b=1;c=d=2$$$$\Rightarrow a+b+c+d+e=6+e=4e\Rightarrow e=2$$$$abcd=5\Rightarrow a=b=c=1;d=5$$$$\Rightarrow a+b+c+d+e=8+e=5e\Rightarrow e=2(\to \leftarrow )$$$$\Rightarrow maximumvalueofe=5$$

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