Fatorial #4

Algebra Level 1

If ( 15 ! + 14 ! + 13 ! 14 ! + 13 ! \frac{15! + 14! + 13!}{14! + 13!} = a) and ((5b - 7)! = 1),

find the sum of all possible values of "a", and add it to the sum of all possible values of "b".

12 21 18 15

Victor Porto by Victor Porto , 22, Brazil

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2 solutions

Abhijith Asokan
Sep 12, 2014

Solving for the value of 'a' we get a=15. Also we get b=8/5 or 7/5, whose sum equal 3. Hence we get sum of "a" plus the possible values of "b"=18.

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a=(15!+14!+13!)/(14!+13!)= [13!(15 14+14+1)]/[13!(14+1)]=(15 14+14+1)/(14+1)=(15*14+15)/(14+1)=(15(14+1))/(14+1)=15, so a=15
1=0!=1! (5b-7)!=1=0!=1! so, 5b-7=0, b=7/5 and 5b-7=1, b=8/5 sum all posisible values of "b" = (7/5)+(8/5)=15/5=3

the sum of all possible values of "a", and add it to the sum of all possible values of "b"= 15+3=18

CMIIW ^_^

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