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# Find three parts of 207 such that they are in increasing order, they form an AP and the product of two smaller parts is 4623.

Given:

Three parts of 207 are in increasing order, they form an AP and the product of two smaller parts is 4623.

To do:

We have to find the three parts.

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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