I am trying to find a solution/s for the following equation:
[imath]x^2 - y^2 -z^2 = 20[/imath]
knowing that x,y,z are consecutive, positive integers of some arithmetic progression.
So we can see it must be decreasing sequence, otherwise the result would be negative.
I wrote following equations:
[math]20 = x^2 -y ^2-z^2 \\ x = y + d\\ y = z + d\\ z = x - 2d\\[/math]then substituting (2) and (3) into (1)
[imath]20 = (z+2d)^2 - (z -d)^2 -z^2[/imath]
But even solving this quadratic equation doesn't get me any closer to the solution. Am I missing some equation or it cannot be solve in this way?
Thank you.
[imath]x^2 - y^2 -z^2 = 20[/imath]
knowing that x,y,z are consecutive, positive integers of some arithmetic progression.
So we can see it must be decreasing sequence, otherwise the result would be negative.
I wrote following equations:
[math]20 = x^2 -y ^2-z^2 \\ x = y + d\\ y = z + d\\ z = x - 2d\\[/math]then substituting (2) and (3) into (1)
[imath]20 = (z+2d)^2 - (z -d)^2 -z^2[/imath]
But even solving this quadratic equation doesn't get me any closer to the solution. Am I missing some equation or it cannot be solve in this way?
Thank you.