Question

the sum of the three number in ap is 21 and their product is 231 find the numbers

Answer 1

Let the AP is (a-d), a, (a+d)
(a-d)+a+(a+d) =21
3a=21
a=7
(a-d)×a×(a+d)=231
(a×a-d×d) ×a=231
(7×7-d×d)×7=231
(7×7-d×d)=231÷7
(7×7-d×d)=33
d×d=49-33
d×d=16
d=4
Hence, the A. P. is 3, 7, 11.

Answer 2

3, 7, 11

Step-by-step explanation:

Let we have an AP as (a-d),a,(a+d)

The sum of the three number in AP is 21 it means,

$a-d+a+a+d=21\\\\3a=21\\\\a=7$

First term of the AP is 7

The product of three numbers is 231. It means,

$(a-d)\times a\times (a+d)=231$

Put a = 7 in above equation :

$(7-d)\times 7\times (7+d)=231\\\\(7-d)\times (7+d)=33\\\\(7)^2-d^2=33\\\\49-33=d^2\\\\d=4$

So, the numbers are : (7-4), 7, (7+4) or 3,7,11

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