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Here we are given (x-9)^1/4 - (x+2)^1/3 = -1 and we have to find x!

As factorial is defined only for an integer, the fourth root of x - 9 should be 1 less than the third root of x + 2

We have:

1^4 = 1 , 2^4 = 16 , 3^4 = 81

1^3 = 1, 2^3 = 8, 3^3 = 27

Using these values we try to arrive at the value of x. We see that we can take x = 25 and we get x - 9 = 16 = 2^4 and x + 2 = 27 = 3^3

Also 2 - 3 = -1

Therefore the required value of x! = 25!

Approved by eNotes Editorial Team

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