Question #2ed49

1 Answer
Nov 26, 2017

alpha=1/2
beta=-1/3
gamma=1

Explanation:

let a=1/alpha , b=1/beta , c=1/gamma

=>

4a-b+c=12 => c=12+b-4a
2a+2b+3c=1
5a-2b+6c=22

=>

2a+2b+3*(12+b-4a)=1
5a-2b+6*(12+b-4a)=22

=>

2a+2b+36+3b-12a=1
5a-2b+72+6b-24a=22

=>

-10a+5b=-35
-19a+4b=-50

=>

-2a+b=-7 => b=-7+2a
-19a+4b=-50

=>

-19a+4*(-7+2a)=-50

=>

-19a-28+8a=-50

=>

-11a=-22 => a=2

=>

b=-7+2*(2)=-3

=>

c=12+(-3)-4*(2)=1

=>

2=1/alpha => alpha=1/2
-3=1/beta => beta=-1/3
1=1/gamma => gamma=1

check:

4/(1/2)-1/(-1/3)+1=8+3+1=12

2/(1/2)+2/(-1/3)+3/1=4-6+3=1

5/(1/2)-2/(-1/3)+6/1=10+6+6=22