Question

Find the three numbers in AP whose sum is 15 and product is 80.

 

Answer 1

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).