SOLUTION: The square of a natural number is four more than two times another natural number. The second number is two less than three times the first number. Determine the two natural number

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Question 320066: The square of a natural number is four more than two times another natural number. The second number is two less than three times the first number. Determine the two natural numbers algebraically.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let the natural numbers be x & y
x^2=2y+4
..
y+2 /3 =x
(y+2)^2/9=x^2
2y+4=(y+2)^2 /9
18y+36=y^2+4y+4
y^2-14y-32=0
y^2-16y+2y-32=0
y(y-16)+2(y-16)=0
(y+2)(y-16)=0
y=-2 OR 16
Plug the value of y in the equation y+2 /3 =x
when y=-2 x=0
..
when y=16 x=6