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let the there numbers be
a,b,c
As they are in continued
Proportion
b
2
=ac
mean is 12
∴b=12
So, 12
2
=ac
144=ac
c=144/a
Sum of two number is
a+c=26
a+
a
144
=26
Solving,
=a
2
+144−26a=0
=a
2
−18a−8a+144=0
=a(a−18)−8(a−18)=0
=(a−18)(a−8)=0
∴a=18 or a=8
c=8 c=18
∴ The numbers are :-
8,12,18 or 18,12,8
hope this helps you
thanks
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