Question 86

If $$(\frac{x}{y})^{a-4}=(\frac{y}{x})^{2a-5}$$, then what is the relation between x and y?

Solution

Given : $$(\frac{x}{y})^{a-4}=(\frac{y}{x})^{2a-5}$$

=> $$(\frac{y}{x})^{4-a}=(\frac{y}{x})^{2a-5}$$

=> $$4-a=2a-5$$

=> $$2a+a=5+4=9$$

=> $$a=\frac{9}{3}=3$$

$$\therefore$$ $$(\frac{x}{y})^{3-4}=(\frac{y}{x})^{2(3)-5}$$

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

=> $$\frac{y}{x}=\frac{y}{x}$$

Thus, relation cannot be established.

=> Ans - (B)

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