Question

divide 45 into three parts which are in AP and the product is 300 find ap

Answer 1

let the AP be

a, a+d, a+2d

so 3a + 3d = 45
a+d = 15 ---> d = 15-a

and

a(a+d)(a+2d)=300
a(a^2 + 3ad + 2d^2) = 300
a(a^2 + 3a(15-a) + 2(15-a)^2) = 300
a(a^2 + 45a - 3a^2 + 450 - 60a + 2a^2) = 300
a(- 15a + 450) = 300
-15a^2 + 450a - 300 = 0
a^2 - 30a + 20 = 0
a = (30 ± √820)/2
= 15 ± √205 = 29.3178.. or .68217...

then d = 15-a
d = -14.317... or d = +14.317..

your 3 numbers are:
29.318, 15, .682
or
.682, 15, 29.318 , which are just the same numbers reversed

check:
29.318+15+.682 = 45
(29.318)(15)(.682) = 299.999. close enough