Question 633036
Let the childrens' age be x & y  , x >y
Father's age 2x+4y

xy= 48

Harmonic mean 
{{{(2/(1/x+1/y))}}}


{{{(2/((x+y)/xy)))}}}=6


{{{2xy/(x+y) =6}}}


xy = 48

{{{2*48/(x+y)}}}= 6

{{{x+y= 96/6}}}

x+y = 16
xy = 48


x=48/y

{{{48/y + y = 16}}}

multiply equation by y
{{{48+y^2=16y}}}

{{{y^2-16y+48=0}}}

{{{y^2-8x-6x+48=0}}}

{{{y(y-8)-6(y-8)=0}}}

(y-8)(y-6)=0

y= 8 OR 6

xy = 48 
therefore x=8 

The sons' ages are 8 & 6

Father's age 2x+4y  -> 2*8+4*6

=40 years

m.ananth@hotmail.ca