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/sci/ - Science & Math

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10216245 No.10216245 [Reply] [Original]

Can I get a hint for part (a)?

>> No.10216255

>>10216245
Since there is no floor, x has to be rational -- i.e. x = 2001/n

Where Floor[x * Floor[ x * Floor[x] ] ] = n
2001/286 works

>> No.10216257

Trial and error. f(x) = x^4 on the integers, and f is increasing, so you don't need to go any higher than say 10

>> No.10216262

>>10216255
>>10216257

ty!!!

>> No.10216283

>>10216245
It has to be a rational number of the form 2001/n since the result of the floor function is an integer.

It has to be between 6 and 7 since 2001 is between 6^4 and 7^4. Start checking at the closest number below 7 since the floor function is going to keep reducing the numbers being multiplied. Since 2001/7 is closest to 286 that is the first n we check. It works, so the solution is 2001/286.

2002/7 = 286 so f(2002/286) > 2002. f(2002/287) < 2002 so there is no solution.

>> No.10216436

>>10216245
F(x) = 2001 + 0*x

>> No.10216438

>>10216436
Part B:

2002 = 2001 + 0*x
1 = 0*x

Contradiction.

This was the easiest fucking assignment of ALL TIME

>> No.10216439

>>10216245
Do your own homework