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Question
Find the three numbers in AP whose sum is 15 and product is 80.
Solution
Let the required numbers be (a -d ),a and (a + d).
Then (a-d) +a + (a+d)=15
⇒ 3a =15
⇒a=5
Also, (a-d) . a . (a+d) = 80
⇒` a(a^2 - d^2 ) = 80`
⇒`5 (25 - d^2 ) = 80 `
⇒` d^2 = 25-16=9 `
⇒ `d =+- 3`
Thus a= 5 and `d = +- 3`
Hence, the required numbers are (2,5 and 8) or (8,5 and 2).
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