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Split 207 into three parts such that these are in A.P. and the product of the two smaller parts is 4623.
Given:
Split 207 into three parts such that these are in A.P. and the product of the two smaller parts is 4623.
To do:
We have to find the numbers.
Solution:
Let the three parts of the number 207 be $(a – d), a$ and $(a + d)$, which are in A.P.
According to the question,
Sum of the three parts $= 207$
$a – d + a + a + d = 207$
$3a = 207$
$a = \frac{207}{3}$
$a=69$
Product of the two smaller parts $= 4623$
This implies,
$a (a – d) = 4623$
$69 (69 – d) = 4623$
$69 – d = \frac{4623}{69}$
$69 – d =67$
$d = 69 – 67$
$d= 2$
Therefore,
First part $= a – d = 69 – 2 = 67$,
Second part $= a = 69$
Third part $= a + d = 69 + 2 = 71$
Hence, the required three parts are 67, 69, 71.
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