asdf123
  • asdf123
If x and y are integers, list ALL of the ordered pairs (x,y) such that the product of x and y equals the sum of x and y.
Mathematics
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asdf123
  • asdf123
If x and y are integers, list ALL of the ordered pairs (x,y) such that the product of x and y equals the sum of x and y.
Mathematics
jamiebookeater
  • jamiebookeater
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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myininaya
  • myininaya
xy=x+y means xy-y=x means y(x-1)=x means y=x/(x-1). So any ordered pair in this form (x,x/(x-1)) is an oder pair who has its product =to its sum. example: let x=2. Then we have (2,2). We know it holds for (2,2) since 2+2=2(2). How about for x=3. Then we have (3,3/2) We know it holds for (3,3/2) since 3+3/2=3(3/2)
myininaya
  • myininaya
(x,y) product means x*y sum means x+y product=sum means xy=x+y Solve for either y or x. I chose y in the above. xy-y=x+y-y subtracted y on both sides y(x-1)=x now dividing x-1 on both sides gives y=x/(x-1) The order pair who has it sum=to its product is (x,x,/(x-1))
myininaya
  • myininaya
oops thats suppose to read (x,x/(x-1))

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asdf123
  • asdf123
im so confused lol
myininaya
  • myininaya
what part?
asdf123
  • asdf123
(x,x/(x-1))
asdf123
  • asdf123
is dat the answer?
myininaya
  • myininaya
yes (x,x/(x-1)) , x does not equal 1
asdf123
  • asdf123
k
myininaya
  • myininaya
x+y=x/(x-1)={x(x-1)+x}/(x-1)=(x^2-x+x)/(x-1)=x^2/(x-1) xy=x(x/(x-1)=x^2/(x-1) so x+y=xy we just checked our work
myininaya
  • myininaya
i missed my x in x+y its suppose to read x+y=x+x/(x-1)=[x(x-1)+x]/(x-1)=[x^2-x+x]/(x-1)=x^2/(x-1)

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