Question

there are three numbers in AP whose sum is 36 and the product is 1680 find the numbers​

Answer 1

Answer:

14,10,12

Step-by-step explanation:

let the three numbers in ap

(a+d);(a-d);a

given their sum is 36

:a+d+a-d+a=36

d and-dwill be cancelled

:3a=36

a=36/3

a=12......(1)

Also given that their product is 1680

(a+d)(a-d)(a)=1680

a^2-d^2(a)=1680. (a+b)(a-b)=a^2-b^2

12^2-d^2(12)=1680. (from 1)

144-d^2(12)=1680

144-d^2=1680/12

144-d^2=140

144=140+d^2

d^2=144-140

d^2=4

d=√4

d=2

a=12,d=2

:12,14,16,18............ is the series

and the numbers are 14,10,12

Answer 2

Step-by-step explanation:

let the three number a+d,a,a-d

sum

a+d+a+a-d=36

3a=36

a=12

product

(a+d)(a)(a-d)=1608

(12+d)(12)(12-d)=1608

144+12d(12-d)=1608

144+144d-12d^2=1608

12d^2-144d+1464=0

÷12

d^2-12d+122

by factorize

you get d

There is some mistakes in question