Question 39

If $$2x+\frac{1}{2x}=2$$, then what is the value of $$\sqrt{2(\frac{1}{x})^4+(\frac{1}{x})^5}$$ ?

Solution

Expression : $$2x+\frac{1}{2x}=2$$

=> $$\frac{4x^2+1}{2x}=2$$

=> $$4x^2+1=4x$$

=> $$4x^2-4x+1=0$$

=> $$(2x-1)^2=0$$

=> $$2x-1=0$$

=> $$x=\frac{1}{2}$$

=> $$\frac{1}{x}=2$$

To find : $$\sqrt{2(\frac{1}{x})^4+(\frac{1}{x})^5}$$

= $$\sqrt{2(2)^4+(2)^5}$$

= $$\sqrt{32+32}=\sqrt{64}=8$$

=> Ans - (D)

Create a FREE account and get: