<PRE><B>Question 1099257</B>
Three no are in continued proportion .if mean proportional is 12 and sum of other two is 26 then find the numbers

a/b = b/c

b=12
a/12=12/c

ac = 144
a =144/c

a+c =26

substitute a

144/c +c =26

multiply equation by c

144 +c^2 = 26c

c^2-26c+144=0

c^2-26c=-144
Add 169 to both sides

c^2-26c +169 =169- 144

(c-13)^2= 25


take the square rooton both sides

(c-13)=+ /- 5

either c-13 = 5 or c-13 = -5

c= 18 or c= 8

ac =144

a = 144/18   or 144/8

a= 8 or 18

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