Question

A finite sequence of numbers is called AWESOME if each subsequent member of the sequence, except the first one, is larger than the previous one and if the

product of all the members of that sequence is a perfect square. For example, sequence 2, 6, 27 is an AWESOME sequence. Determine the natural numbers x and y such that the sequence 28, x, y, 65 is an AWESOME sequence.

Answer 1

The answer is "28, 35, 52, 65"

Explanation:

Calculating the x,y:

`\to x< y<65\\\\\to 65 * 28 xy=13 * 5xy * 7 * 2^2\\\\x=13 \\\\y=5 * 7= 35\\\\`

When

or

`x=35\\\\y= 13 * 2^2=13 * 4 =52`

So, the final answer is "28, 35, 52, 65".