Find two integers whose sum is 11 and product is 18

9,2 and 2,9

Step-by-step explanation:

x+y=11

xy=18

Since they are asking for integers you can simply look through and see what integers multiply out to 18 and then check if they add up to 11. The answers for x and y are 9 and 2. but 9 can be for y as well and 2 can be for x.

How to solve it algebraically

18/y=x

x+y=11(insert 18/y for x)

18/y+y=11(factor it)

(y^2+18)/y=11(multiply both sides by y)

y^2+18=11y (subtract both sides by 11y)

y^2-11y+18=0

complete the square

y^2-11y    = -18

(-11/2)^2=121/4 (add in on both sides)

y^2-11y+121/4=49/4

(y-11/2)^2=49/4 (square root both sides)

y-11/2=±7/2

y=11/2±7/2

y=9 or y=2

so

x=9 or x=2

Hope this helps :)

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