Спримером: log3 (x-3)+log3 2=log 2 10 !

Question

Алгебра: Спримером: log3 (x-3)+log3 2=log 2 10 !

gfjew56df · Accepted Answer

A(из n по m) = n!/(n-m)!;
1) (n!/(n-7)!) + (n!/(n-5)!) = 91*n!/(n-5)!,
(1/(n-7)!) = 90/(n-5)!,
(n-5)!/(n-7)! = 90,
(n-6)*(n-5) = 90;
n^2 - 11n + 30 - 90 = 0;
n^2 - 11n - 60 =0;
D = 11^2 + 4*60 = 121 + 240 = 361 = 19^2;
n1 = (11-19)/2 = -8/2 = -4, не год, т.к. n - целое положительное.
n2 = (11+19)/2= 30/2 = 15.
ответ. 15.
2) (n!/(n-7)!) - (n!/(n-5)!) = 109*n!/(n-5)!;
(1/(n-7)!) = 110/(n-5)!;
(n-5)!/(n-7)! = 110;
(n-6)*(n-5) = 110;
n^2 - 11n + 30 - 110 = 0;
n^2 - 11n - 80 = 0;
D = 11^2 + 4*80 = 121+320 = 441 = 21^2;
n1 = (11-21)/2= -10/2 = -5<0; не годится.
n2 = (11+21)/2 = 32/2 = 16.
ответ. 16.

MOGZ ответил