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Find all ordered pairs of real nubmers (a,b) for which 3*sqrt(x - 2y) + 3/sqrt(x - 2y) = 10 and x = ay + b.

 Dec 8, 2019
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\(3\sqrt{x - 2y}+\dfrac{3}{\sqrt{x-2y}}=10\\ 3\left(\sqrt{x - 2y}\right)^2-10\sqrt{x-2y}+3=0, x \neq 2y\\ \sqrt{x - 2y} = \dfrac{1}{3} \text{ or }\sqrt{x - 2y} = 3\\ x - 2y = \dfrac{1}{9}\text{ or }x - 2y = 9\\ (a - 2)y + b = \dfrac{1}{9}\text{ or }(a - 2)y + b = 9\\ \text{Assuming the above equations are true for all values of }y,\\ (a, b)=\left(2,\dfrac{1}{9}\right)\text{ or }(2,9)\)

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 Dec 8, 2019
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Hey max smiley

Guest Dec 8, 2019
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Hello :)

MaxWong  Dec 8, 2019
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Hows school?

Guest Dec 8, 2019

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