Question

Three numbers are A. P. If the sum of these number br 27 and the product 648 find the numbers

Answer 1

let. three no are (a-d),(a),(a+d)
a-d+a+a+d=27
3a=27
a=9
then (9-d),(9),(9+d )in. ap
(9-d)×(9)×(9+d)=648
((9)²-(d²))×9=648

(81-d²)×9=648
729-9d²=648
-9d²= -81
d²=9
d=3
hence number are (9-3),(9),(9+3)=6,9,12

hope it's helps

Answer 2

Three numbers are (a - d), (a), (a + d)
Therefore sum = (a - d) + (a) + (a + d) = 27
3a = 27
a = 27 / 3
a = 9
Product is (a - d) x (a) x (a + d) = 648
= (a^2 - ad) (a + d) = 648
= a^3 +a^2d - a^2d - ad^2 = 648
= a(a^2 - d^2) = 648
Place value of a
9(81 - d^2) = 648
81 - d^2 = 72
- d^2 = 72 - 81
- d^2 = - 9
d^2 = 9
d = 3
The numbers are
a - d = 9 - 3
= 6
2nd number = 9
3rd number = (a + d)
= 9 + 3
= 12

Therefore, the number are 6, 9 & 12.