solve-inside-N-2-x-x-1-4y-y-1-

Question Number 73033 by mathmax by abdo last updated on 05/Nov/19

s o l v e i n s i d e N^{2} x (x + 1) = 4 y (y + 1)

Answered by mind is power last updated on 05/Nov/19

\Leftrightarrow 4 x (x + 1) = 16 y (y + 1)

\Rightarrow x ⩾ y ⩾ 0

\Leftrightarrow {(2 x + 1)}^{2} - 1 = {(4 y + 2)}^{2} - 4

\Rightarrow {(4 y + 2)}^{2} - {(2 x + 1)}^{2} = 3

\Rightarrow (4 y - 2 x + 1) (4 y + 2 x + 3) = 3

\Rightarrow {\begin{cases} 4 y - 2 x + 1 = 1 \\ 4 y + 2 x + 3 = 3 \end{cases}

\Rightarrow x = y = 0