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(n-4)(n-5)(n-6)(n-7) = (n-4)(n-7)*(n-5)(n-6)=(n^2–11n+28)*(n^2–11n+30); n^2–11n+29 = t;
(t-1)*(t+1) = 360; t^2–1 = 360; t^2 = 361;
1)t = 19 or 2)t = -19
1)n^2–11n+29 = 19
n^2–11n+10 = 0
n = 1 or n = 10
2)n^2–11n+29 = -19
n^2–11n+48 = 0
n^2–2*11n/2+(11/2)^2+48-(11/2)^2 = 0
(n-11/2)^2+17,25 = 0
no solutions
Answer: n = 1, n = 10.
(t-1)*(t+1) = 360; t^2–1 = 360; t^2 = 361;
1)t = 19 or 2)t = -19
1)n^2–11n+29 = 19
n^2–11n+10 = 0
n = 1 or n = 10
2)n^2–11n+29 = -19
n^2–11n+48 = 0
n^2–2*11n/2+(11/2)^2+48-(11/2)^2 = 0
(n-11/2)^2+17,25 = 0
no solutions
Answer: n = 1, n = 10.
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