Question

There are three numbers in A.P. whose sum is 60 and sum of cubes is 24480 then the product of these numbers is:

Answer 1

Answer:

Let the three numbers be x, y, and z.

Then, x + d = y, y + d = z.

Now, x + y + z = 60

x + (x + d) + [(x + d) + d] = 60

3(x + d) = 60

x + d = 20

Now, $x^{3} + (y)^{3}  + z^{3} = 24480$

$x^{3} + (x + d)^{3}  + (x + 2d)^{3} = 24480$

$x^{3} + 20^{3} + (20 + d)^{3} = 24480$

$x^{3} + 8000 + (8000 + 1200x + 60x^{2} + d^{3} = 24480$

$x^{3} + 60x^{2} + 1200x + d^{3} = 8480$

$x^{3} + d^{3} = (x + d)(x^{2} -xd + d^{2})$

So,

$x^{3} + 60x^{2} + 1200x + d^{3} = 8480$

$(x + d)(x^{2} -xd + d^{2}) + 1200x + 60x^{2}  = 8480$

Since x + d = 20,

$x^{2} - xd + d^{2} + 60x + 3x^{2} = 4240$

Sorry, this is all I could think of :(