the sum of three numbers in AP is 12 and the sum of their cubes is 288 find the numbers
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20
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avivekanandhan19:
The ap is 4,6,2 if d=-2 and the ap is 4,2,6 if d=2
Answered by
10
let the nber be x,y
ATQ,
x+y=12. .......eq1
x^3+y^3=288.......eq2
now (x+y)^3=12^3
x^3+y^3+3xy(x+y)=1728
288+3xy=1728
36xy=1728-288
xy=40
we know that (a+b)^2=
a^2+b^2+2ab
so
12^2=x^2+y^2+2*40
x^2+y^2=144-80
x^2+y^2=64
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