Find all pairs of natural numbers (x;y) that satisfying condition please>?

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Answer 1 · 2018-02-25T14:42:06

Read below.

Let's multiply the equation by #xy#

#xy[1/x+1/y=1/2017]#

#=>cancelxy*1/cancelx+xcancely*1/cancely=xy*1/2017#

#=>y+x=(xy)/2017# multiply both sides by 2017

#=>2017y+2017x=xy#

#=>2017x=xy-2017y#

#=>2017x=y(x-2017)#

#(2017x)/(x-2017)=y#

Similarly, we can also get:

#(2017y)/(y-2017)=x#

Notice that these two are undefined when #x=2017# or #y=2017#

Also, from our original equation, we can see that #x=0# and #y=0# will make the equation undefined.

Therefore, the set is #(x,(2017x)/(x-2017))# for a given value of #x# as long as #x!=0# and #x!=2017#.

For example, when #x=5#:

#y=(2017*5)/(5-2017)# When you solve this, you get:

#y~~-5.01242544733#