All the pairs (x, y) that satisfy the inequality 2^ ^2 x-2 x+5 , 1 4 ^2 y 1 also satisfy the equation

Step-by-step solution

2^ ^2 x-2 x+5 2^ -2 ^2 y 1 aligned & 2^ ^2 x-2 x+5 2^ 2 ^2 y & ^2 x-2 x+5 2 ^2 y & ( x-1)^2+4 2 ^2 y aligned aligned & ( x-1)^2+4 4 ^4 y & -1 y 1 & 0 ^4 y 1 & For y= 1 (maximum value) & ( x-1)^2+4=4 aligned aligned & ( x-1)^2=0 & x=1 & x=| y| aligned