Help with a math problem plz. Problem: ab=3, bc=4, ac=5, find all possible (a,b, c). plz show work. thx?

ab=3 means b=3/a


ac=5 means c = 5/a


so bc=4 means (3/a)(5/a) = 4 or a = 15/4





b = 3/a = 3*(4/15) = 12/15 = 4/5





c = 5/a = 5*(4/15) = 4/3.





This is one combination, look for others.

Help with a math problem plz. Problem: ab=3, bc=4, ac=5, find all possible (a,b, c). plz show work. thx?
sorry...can't remember my algebra
Reply:ab = 3 so a = 3/b


bc = 4 so c = 4/b


ac = 5 so c = 5/a


c = c so 4/b = 5/a or a/5 = b/4 or a = 5b/4 = 3/b


so that b^2 = 12/5, b = 2sqr[3/5]


a = 3/b = 3/(2sqr[3/5])


c = 4/b = 4/(2sqr[3/5])
Reply:ab=3, bc=4, ac=5


transpose equation 1


b=3/a


sub into equation 2


(3/a)(c)=4


transpose equation 3


a=5/c


sub into derived equation


3/(5/c)*c=4


3c/5*c=4


3c^2/5=4


3c^2=20


c^2=20/3


c=2.58





since bc=4


b=4/2.58


=1.55





since ac=5


a=5/2.58


=1.94


so a=1.94, b=1.55, c=2.58





for another solution, take the negative squre root value of c, instead of the positive, and sub into formulas again.
Reply:Multiplying all three together, you have:





(abc)^2 = 60





taking the square root gives:





abc = 2 sqrt(15) or -2 sqrt(15).





So c = abc / ab = 2 sqrt(15) / 3 or - 2sqrt(15) / 3


b = abc / ac = +- 2 sqrt(15) / 5


a = abc / bc = +- sqrt(15) / 2