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Question
Find two numbers whose mean proportional is 18 and the third proportional is 486.
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Solution
Let a and b be the two numbers, whose mean proportional is 18.
`therefore "ab" = 182 => "ab" = 324 => "b" = 324/"a"` ......(i)
Now, third proportional is 486
∴ a : b : : b : 486
⇒ b2 = 486 a
⇒ `(324/"a")^2` = 486 a
⇒ `(324)^2/"a"^2` = 486 a
⇒ `"a"^3 = (324 xx 324)/486`
⇒ a3 = 216
⇒ a = 6
b = `324/"a" = 324/6 = 54`
Therefore, numbers are 6 and 54 .
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