1.

\( x \) and \( y \) are Natural no's when \( x y-4=2 x+y \). Find pairs of \( (x, y) \).

Answer»

\(xy - 4 = 2x + y\)

⇒ \(y = \frac{4+2x}{x - 1}\)

\(= \frac{2(x + 2)}{x -1}\)

\(=2\left(1 + \frac3{x - 1}\right)\)

\( = 2 + \frac6{x -1}\)

Hence, if x = 2, 3, 4 & 7 then y becomes natural numbers.

Hence, (x, y) pairs are (2, 8), (3, 5), (4, 4), (7, 3).



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