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The value of \( \sqrt{\frac{x}{y}+2+\frac{y}{x}}= \).1) \( \frac{x}{\sqrt{y}}+\frac{\sqrt{y}}{x} \)2) \( \frac{x}{y}+\frac{y}{x} \)3) \( \sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}} \)4) \( \frac{\sqrt{x}}{y}+\frac{y}{\sqrt{x}} \) |
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Answer» \(\sqrt{\frac xy + 2+\frac yx}\) = \(\sqrt{\frac{x^2+2xy+y^2}{xy}}\) = \(\sqrt{\frac{(x+y)^2}{xy}}=\frac{x+y}{\sqrt{xy}}\) = \(\frac{\sqrt x}{\sqrt y}+\frac{\sqrt y}{\sqrt x}\) = \(\sqrt{\frac xy}+\sqrt{\frac yx}\) |
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