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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

$8$

Vedclass · Answer

(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 $\sqrt{2(\frac{1}{x})^4 + (\frac{1}{x})^5}$?

Similar Questions

Find the value of $k$ if $f(x) = x^{3} - kx^{2} + 11x - 6$ and $(x - 1)$ is a factor of $f(x)$.

Factorize: $45 a^{3} b + 5 a b^{3} - 30 a^{2} b^{2}$

If $a-b=1$ and $ab=6$,then what is the value of $(a^3-b^3)$?

When $(x^{3}-2 x^{2}+p x-q)$ is divided by $(x^{2}-2 x-3)$,the remainder is $(x-6)$. The values of $p$ and $q$ are:

If $x+y+z=0,$ what will be the value of $\frac{x^{2}+y^{2}+z^{2}}{x^{2}-y z} ?$

Vedclass Test Series

Exam Paper Generator

Online Exam Module