If 2x + frac{1}{2x} = 2,then what is the valu | vedclass

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(D) Given the equation: $2x + \frac{1}{2x} = 2$.Multiply the entire equation by $2x$ to clear the denominator: $4x^2 + 1 = 4x$.Rearrange the terms to

Vedclass · Accepted Answer

$8$

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(D) Given the equation: $2x + \frac{1}{2x} = 2$.Multiply the entire equation by $2x$ to clear the denominator: $4x^2 + 1 = 4x$.Rearrange the terms to form a quadratic equation: $4x^2 - 4x + 1 = 0$.This is a perfect square trinomial: $(2x - 1)^2 = 0$.Solving for $x$: $2x - 1 = 0$,which gives $x = \frac{1}{2}$.Now,substitute $x = \frac{1}{2}$ into the expression $\sqrt{2(\frac{1}{x})^4 + (\frac{1}{x})^5}$.Since $\frac{1}{x} = 2$,the expression becomes $\sqrt{2(2)^4 + (2)^5}$.Calculate the powers: $2^4 = 16$ and $2^5 = 32$.Substitute these values: $\sqrt{2(16) + 32} = \sqrt{32 + 32} = \sqrt{64}$.The final value is $8$.

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

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