Solve for n (a positive integer) in each equation:
(1) n! = 8n^4 + 15n^3 - 4n^2 + 15n + 8
(2) n! = 9n^4 + 4n^3 + n^2 + 1344
Both analytic and computer solutions welcome.
Asking Wolfram Alpha to
solve n! = 8n^4 + 15n^3 - 4n^2 + 15n + 8
and
solve n! = 9n^4 + 4n^3 + n^2 + 1344
in each instance gives the solution in integers to be 8.
Verification in a Matlab session, results in 40320 for each of the LHS and RHS's:
>> n=8
n =
8
>> 9n^4 + 4n^3 + n^2 + 1344
9n^4 + 4n^3 + n^2 + 1344
?
Invalid expression. Check for missing multiplication operator,
missing or unbalanced delimiters, or other syntax error. To
construct matrices, use brackets instead of parentheses.
Did you mean:
>> 9*n^4 + 4*n^3 + n^2 + 1344
ans =
40320
(It was easier to allow Matlab to supply the *'s than to insert them myself.)
>> factorial(n)
ans =
40320
>> 8n^4 + 15n^3 - 4n^2 + 15n + 8
8n^4 + 15n^3 - 4n^2 + 15n + 8
?
Invalid expression. Check for missing multiplication operator,
missing or unbalanced delimiters, or other syntax error. To
construct matrices, use brackets instead of parentheses.
Did you mean:
>> 8*n^4 + 15*n^3 - 4*n^2 + 15*n + 8
ans =
40320
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Posted by Charlie
on 2022-07-02 10:32:34 |
very computerized solution
