Question

divide 24 in 3 parts such that they are in arthematic progession and their product is 240

Answer 1

I'm thinking that the product of the 3 numbers is 440.........
Let the three numbers be (a-d), a, (a+d).
It it given that the three numbers are in AP and the sum of the numbers is 24.
So,(a-d)+a+(a+d) =24
=>a-d+a+a+d=24
=>3a=24
=>a=24/3=8
It is also given that the product of the numbers are 440.
So,(a-d)(a)(a+d)=440
=>a(a^2-d^2)=440
=>a^3-ad^2=440
=>8^3-8d^2=440
=>-8d^2=440-512
=>-8d^2=-72
=>8d^2=72
=>d^2=72/8
=>d^2=9
=>d=root 9
=+3 or -3
If, d=3
So,a-d=8-3=5
a=8
a+d=8+3=11
If, d=-3
So,a-d=8-(-3)=11
a=8
a+d=8+(-3)=5