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Algebra Level 3

Find the sum of all integer x x satisfying x x x = ( x x ) x x^{x^{x}}=(x^{x})^{x} .

1 3 2 0

Ishtiaque Ahmed Sayef by Ishtiaque Ahmed Sayef , 24, Bangladesh

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1 solution

Hana Wehbi
Mar 2, 2020

If we plug in x = 1 x =1 the equation is true and for x = 2 x=2 as well. Beyond these two values, there are no other solutions. We can also verify this by graphing and detecting the intersecting points. Thus, the sum of solutions is 3 3 .

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What's about x = − 1 x=-1 ?

Ishtiaque Ahmed Sayef - 1 year, 3 months ago

the question required the SUM of all integer x that satisfy........and not the number of integers which satisfy

Ritabrata Roy - 1 year, 3 months ago

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Ok, I will fix it.

Hana Wehbi - 1 year, 3 months ago

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