If y = √x÷a + √a÷x , prove that 2xy dy/dx = (x/a - a/x) .

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y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}

2 x y \frac{d y}{d x} = \frac{x}{a} - \frac{a}{x}

y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}

2 x y \frac{d y}{d x} = (\frac{x}{a} - \frac{a}{x})

\frac{d y}{d x} + \frac{y^{2} + y + 1}{x^{2} + x + 1} = 0

(x + y + 1) = A (1 - x - y - 2 x y)

A

y = \sqrt{\frac{x}{a} +} \sqrt{\frac{a}{x},} p r o v e t h a t 2 x y \frac{d y}{d x} = (\frac{x}{a} - \frac{a}{x})

\sqrt{x} + \sqrt{y} = \sqrt{a}

\frac{d y}{d x} = - \sqrt{\frac{y}{x}}

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