Problem / game
First name
Sasi
School
Kimberley STEM College
Country
Age
16
Email address
sasivalai@gmail.com
x + y < 1 + xy
xy – x – y + 1 > 0
x(y – 1) – (y – 1) > 0 (take out a factor of y - 1)
(x – 1)(y – 1) > 0 (factorise the LHS)
If 0 < x < 1 and 0 < y < 1, x – 1 and y – 1 will both be less than 0, so (x – 1)(y – 1) will be greater than 0. Therefore the inequality is true when 0 < x < 1 and 0 < y < 1.