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Question

Find three numbers in A.P., whose sum is 15 and the product is 80.

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Solution

letad,a,a+darethreetermsofanAP

accordingtotheproblemgiven,

sumoftheterms=15

ad+a+a+d=15

3a=15

a=153

a=5

product=80

(ad)a(a+d)=80

(a²d²)a=80

(5²d²)5=80

25d²=80/5

25d²=16

d²=9

d²=3²

d=±3

Therefore,a=5,d=±3

required3termsare

ad=53=2

a=5

a+d=5+3=8

(2,5,8)or(8,5,2)

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