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Question
Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623.
Solution
Let the three parts of the number 207 are (a – d), a and (a + d), which are in AP.
Now, by given condition,
⇒ Sum of these parts = 207
⇒ a – d + a + a + d = 207
⇒ 3a = 207
a = 69
Given that,
Product of the two smaller parts = 4623
⇒ a(a – d) = 4623
⇒ 69 . (69 – d) = 4623
⇒ 69 – d = 67
⇒ d = 69 – 67 = 2
So, first part = a – d = 69 – 2 = 67,
Second part = a = 69
And third part = a + d = 69 + 2 = 71
Hence, required three parts are 67, 69, 71.
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