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1 year ago

Sum of three numbers in an as is 33 and the sum of thier cubes is 5049.find the numbers

Mathematics

1 answer:

Alex73 [517]1 year ago

6 0

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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