the sum of three number is ap is - 24 and their product is 288 find the numbers
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let 3 numbers be a-d a a+d
according to the first condition
a-d+a+a+d=-24
3a=-24
a= -8
according to the second condition
(a-d)×a×(a+d)=288
(a^2-d^2)×a=288
a^3-ad^2=288
substituting a= - 8
-512+8d^2=288
8d^2=288+512
8d^2=800
d^2=100
d=10
the numbers are
a-d=-18
a=-8
a+d=2
according to the first condition
a-d+a+a+d=-24
3a=-24
a= -8
according to the second condition
(a-d)×a×(a+d)=288
(a^2-d^2)×a=288
a^3-ad^2=288
substituting a= - 8
-512+8d^2=288
8d^2=288+512
8d^2=800
d^2=100
d=10
the numbers are
a-d=-18
a=-8
a+d=2
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