SOLUTION: find the three numbers in an arithmetic progression whose sum is 48 and the sum of their squares is 800

One can present the three consecutive terms of the AP as

x -d, x, x + d,

where x is the mid term and d is the common difference.

Then the sum of the tree terms is 3x, and you can easily find a from the equation

3x = 48,

which implies x =  = 16.

Now the sum of squares of the tree terms is

 =  =  = .

It gives you an equation to find d:

 =   --->   =  = 32  --->   =  = 16.

Hence, d = +/- 4.

It gives the AP terms as  12, 16 20,   or   20, 16, 12.

Answer. AP terms are  12, 16 20,   or   20, 16, 12.