If (x-y)P2=56,then X+y =
Answers
Step-by-step explanation:
If 2^x-y=56, what is the value of x+y?
We shall treat it as a Diophantine equation and find the integer solutions only.
Take x=6, y=8, then the relation is satisfied, so that x+y=14, is a solution. But we could also take x=7, and y=72 because 2^7 - 72 =128–72 =56 and so x+y=7+72=79 is another answer.
Each time you increase x by 1, 2^x increases further by 2^x and so you have to increase y by 2^x, and x+y consequently increases by 1+ 2^x. Hence there are infinitely many answers.
Here are a few more solutions,which happen to be negative :
x=0,y=(-55), x+y=(-55), x=1, y=(-54), x+y =(-53), x=2, y=(-52), x+y =(-50), x=3, y =(-48), x+y=(-45), x=4, y=(-40), x+y =(-36) and x= 5, y=(-24), x+y =(-19). Obviously the negative values of x do not give integer solutions.
Hence our first solution is the least positive solution.