Question 72

If $$\sqrt{x+\frac{x}{y}}=x\sqrt{\frac{x}{y}}$$, where x and y are positive real numbers, then y is equal to

Expression : $$\sqrt{x+\frac{x}{y}}=x\sqrt{\frac{x}{y}}$$

=> $$x+\frac{x}{y}=x^2\times\frac{x}{y}$$

=> $$1+\frac{1}{y}=\frac{x^2}{y}$$

=> $$\frac{1}{y}(x^2-1)=1$$

=> $$y=x^2-1$$

=> Ans - (B)

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