Question

The sum of three numbers is an arithmetic progression is 9 and their product is 24 ,find the number??

Answer 1

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

❥ Let 3 numbers in AP be x , x + 1 and x + 2

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❥ sum = x + x + 1 + x + 2 ➜ 9

↠ 3x + 3 ➜ 9

↠3x ➜ 9 - 3

↠ 3x ➜ 6

↠ x ➜ 6/3

↠ x ➜ 2

↠ (x+1 ) ➜ 3

↠ (x+2) ➜ 4

❥ 2 , 3 and 4 are the 3 numbers required

❥ Product of 3 numbers ↠ 24

❥ 2 , 3 and 4 are 3 numbers

Hence ,

2 , 3 and 4 are 3 numbers.

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Answer 2

Answer:

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Let the three numbers in A.P. be a−d,a, and a+d

According to given information

Sum=(a−d)+(a)+(a+d)=24...(1)

⇒3a=24∴a=8

& Product=(a−d)a(a+d)=440...(2)

⇒(8−d)(8)(8+d)=440

⇒(8−d)(8+d)=55

⇒64−d

2

=55

⇒d

2

=64−55=9

⇒d=±3

Therefore when d=3, the numbers are 5,8,11 and

when d=−3, the numbers are 11,8 and 5.

Thus the three numbers are 5,8 and 11.