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Question
Find two nurnbers whose mean proportional is 12 and the third proportional is 324.
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Solution
Let a and b be the two numbers, whose mean proportional is 12.
∴ ab =122 ⇒ ab = 144 ⇒ b = `144/"a"` ...........(i)
Now, third proportional is 324
∴ a : b : : b : 324
⇒ `(144/"a")^2 = 324 "a"`
⇒ `(144)^2/"a"^2 = 324 "a"`
⇒ a3 = `(144 xx 144)/324`
⇒ a3 = 64
⇒ a = 4
b = `144/"a" = 144/4 = 36`
Therefore, numbers are 4 and 36
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