Question

28. Sum of three numbers in an AP is 21 and their product is 231. Find the numbers.​

Answer 1

Explanation:

let the three numbers be

(a-d) ,(a) and (a+d)

so we have the sum as

a-d+a+a+d=21

3a=21

a=7..............(1)

we have d product as

(a-d)(a)(a+d)=231

(a²-d²)(a)=231

a³-ad²=231..........(2)

subtitue (1) in (2)

we have

(7)³-(7)d²=231

343-7d²=231

343-231=7d²

112=7d²

d²=112/7

d²=16

d=±4

when d=-4

the first number is

a-d=7-(-4)=7+4=11

second number is

a=7

third number

a+d=7+(-4)=7-4=3

when d=4

the first number is

a-d=7-4=3

the second number is

a=7

the third number is

a+d=7+4=11