Question

Rezolvați inecuatia(n-4)!<20(n-6)!

Answer 1

Explicație pas cu pas:

(n-1)(n-2)(n-3)(n-4)<20(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)/:[(n-1)(n-2)(n-3)(n-4)]

1<20(n-5)(n-6)

1<20(n^2-11n+30)

1<20n^2-222n+60

0<20n^2+-222n+59

Aplicam delta

Delta =b^2-4ac

Delta=222^2-4*20*59

Delta=49824

X1=(-b-radical delta) /2a

X1=222-222/2*20

X1=0=n1

X2=(-b+radical delta) /2a

X2=(222+222)/40

X2=444/40

X2=11,1=n2

Deci, avem soluțiile n€{0; 11,1}