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Question
The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers
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Solution
Let the three numbers in A.P. be a – d, a, a + d (d > 0)
Now (a – d) a (a + d) = 224
⇒ a (a2 – d2) = 224 .....(1)
Now, since the largest number is 7 times the smallest
i.e., a + d = 7(a – d)
Therefore, d = `(3"a")/4`
Substituting this value of d in (1), we get
`a(a^2 - (9a^2)/16)` = 224
a = 8
And d = `(3a)/4 = 3/4 xx 8` = 6
Hence, the three numbers are 2, 8, 14.
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