What is $\frac{d y}{d x}$ $(dy)/(dx)$ of $\sqrt{\frac{y}{x}} + \sqrt{\frac{x}{y}} = \sqrt{a} ? ? ?$ $sqrt(y/x)+sqrt(x/y)=sqrta???$

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Answer 1 · 2018-03-03T10:24:37

I am confused something still I answered.

![My http://notebook...](https://useruploads.socratic.org/f7HD0xiERVOGEPbBftUy_New_Doc_2018-03-03_1%5B1%5D.jpg)

I took $a$ $a$ as constant.
Used the rule $ul(bar(|color(red)(d/(dx)(uv)=(v cdot (du)/(dx)-v cdot (dv)/(dx))/v^2))|$

Answer 2 · 2018-03-03T10:37:26

See below.

Making $y = lambda^2 x$ and substituting

$lambda+1/lambda = sqrta$ or

$lambda^2-sqrta lambda + 1 = 0$

now solving for $lambda$

$lambda =1/2( sqrta pm sqrt(a-4))$ so

$y/x = 1/4( sqrta pm sqrt(a-4))^2$

and then

$dy/dx = 1/4( sqrta pm sqrt(a-4))^2$

for $a > 4$

Attached a plot for

$sqrt(y/x)+sqrt(x/y) = 2.3$

enter image source here

What is (dy)/(dx)dydx(dy)/(dx) of sqrt(y/x)+sqrt(x/y)=sqrta???√yx+√xy=√a???sqrt(y/x)+sqrt(x/y)=sqrta???