Question

Sum of the three numbers in an AS is 33 and the sum of their cubes is 5049. find the numbers

Answer 1

The computation shows that the numbers will be 7, 11, and 15.

How to compute the value?

Let the numbers be:

First number = a - d

Second number = a

Third number = a + d

a - d + a + a + d = 33

3a = 33

a = 33/3 = 11

The second condition will be:

(a - d)³ + a³ + (a + d)³ = 5049

a³ - d³ - 3ad(a - d) + a³ + a³ + d³ + 3ad(a + d) = 5049

3a³ + 6a × d² = 5049

Replace a = 11

3 × 11³ + (6 × 11) × d² = 5049

d² = (5049 - 3 × 11³)/6 × 11

d² = 16.

d = ✓16

d = 4

First number = a - d = 11 - 4 = 7

Second number = a = 11

Third number = a + d = 11 + 4 = 15

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