4.
А²m=90
m!/(m-2)!=90
(m-2)!*(m-1)*m/(m-2)!=90
(m-1)*m=90
m²-m-90=0 D=361 √D=19
m₁=10 m₂=-9 ∉
Ответ: m=10.
A³m=56m
m!/(m-3)!=56m
(m-3)!*(m-2)*(m-1)*m/(m-3)!=56m
(m-2)*(m-1)*m=56m
(m-2)*(m-1)*m-56m=0
m*((m-2)*(m-1)-56)=0
m₁=0
(m-2)*(m-1)-56=0
m²-3m+2-56=0
m²-3m-54=0 D=225 √D=15
m₂=9 m₃=-6 ∉
Ответ: m₁=0 m₂=9,
5.
C³m=(4/15)*C⁴m+2 |*15
15*m!/((m-3)!*3!)=4*(m+2)!/((m+2-4)!*4!)
15*(m-3)!*(m-2)*(m-1)*m/((m-3)!*6)=4*(m+2)!/((m-2)!*24)
15*4*(m-2)*(m-1)*m=4*(m-2)!*(m-1)*m*(m+1)*(m-2)/(m-2)!
60*(m-2)*(m-1)*m=4*(m-1)*m*(m+1)*(m+2)
60*(m-2)=4*(m+1)*(m+2)
60m-120=4m²+12m+8
4m²-48m+128=0 |÷4
m²-12m+32=0 D=16 √D=4
Ответ: m₁=8 m₂=4.
5*С³m=C⁴m+2
5*m!/((m-3)!*3!)=(m+2)!/((m+2-4)*4!)
5*4*(m-3)!*(m-2)*(m-1)*m/(m-3)!=(m+2)!/(m-2)!
20*(m-2)*(m-1)*m=(m-1)*m*(m+1)*(m+2)
20*(m-2)=(m+1)*(m+2)
20m-40=m²+3m+2
m²-17m+42=0 D=121 √D=11
m₁=14 m₂=3 ∉.
Ответ:: m=14.