Sum of three numbers is 33 and sum of their cubes is 5049 then three numbers are 7,11,15 or 15,11,7.
As given,
Let a-d, a, a +d be three numbers
Sum =33
⇒a-d + a +a +d =33
⇒ a =11
Sum of cubes= 5049
⇒ (a-d)³ + a +(a +d)³ =5049
⇒ a³ -d³ -3a²d +3ad² + a³ +a³ +d³ +3a²d +3ad² =5049
⇒3a³ + 6ad² = 5049
⇒ d=± 4
Therefore, sum of three numbers is 33 and sum of their cubes is 5049 then three numbers are 7,11,15 or 15,11,7.
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