Question

rezolvati urmatoarele exercitii

Answer 1

7)a)10!/8!+8!/7!=10*9*8!/8!+8*7!/7!=10*9+8=98

c)n!/(n-1)!+n!/(n-2)!=n*(n-1)!/(n-1)!+n*(n-1)*(n-2)!/(n-2)!=n+n(n-1)=n+n²-n=n²

8)a)n!/(n-1)!+(n+1)!/(n-1)!=35
n*(n-1)!/(n-1)!+n(n+1)*(n-1)!/(n-1)!=35
n+n(n+1)=35
n+n²+n-35=0
n²+2n-35=0

n1+n2=-2
n1*n2=-35

n1=-7, nu e posibil, deoarece numarul sub factoria trebuie sa fie pozitiv.
n2=5

S={5}

b)(n+1)!+n!=35(n-1)!
n(n+1)*(n-1)!+n*(n-1)!=35(n-1)!
n(n+1)+n=35
n²+2n-35=0

Analogic cu a)

S={5}

c)(n+1)!=60(n-2)!
n(n+1)(n-1)*(n-2)!=60(n-2)!
n(n+1)(n-1)=60
n(n²-1)=60
n³-n-60=0

Din rezolvarea ecuatiei de gradul 3, obtii o singura solutie correcta:

S={4}.

9)a)7!=1*2*3*4*5*6*7=2*3*4*5*6*7=6*4*5*6*7=24*5*6*7=120*6*7=720*7=5040

b)n!=720
n=6

c)n!≤720
n≤6, n≥0

n∈[0;6]

d)n!<5100
n<7,006, n≥0

n∈[0;7,006)