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
Solution
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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