Without solving for x and y, determine the possible values of x/y, whenever:
x+y=29, and:
x*y=198
WITHOUT solving for x:
Call x/y R
x+y=29 divide both by y
R + 1 = 29/y
y = 29/(R + 1)
x*y=198 divide both by y^2
R = 198/y^2
y^2 = 198/R
y^2 = [29/(R + 1)]^2
R = 198/[29/(R + 1)]^2
R = 198*(R + 1)^2/(29^2)
841*R = 198*(R^2 + 2*R + 1)
198*R^2 + 396*R - 841*R + 198 = 0
198*R^2 - 445*R + 198 = 0
which factors to: (18R-11)(11R-18) = 0
R = x/y: {11/18, 18/11}
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Posted by Larry
on 2022-12-17 09:09:38 |
Solution
