The value of the given expression will be -1.
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition,substraction, multiplication and division.
We have the following expression:-
[tex]2x+\dfrac{1}{2x}=1[/tex]
We need to find the value of
[tex]16x^4+\dfrac{1}{16x^4}=?[/tex]
So by using the given expression:-
[tex]2x+\dfrac{1}{2x}=1[/tex]
By applying the formula
( a + b )² = a² + b² + 2ab
So the solution will be:-
[tex]2x+\dfrac{1}{2x}=1\\\\\\(2x+\dfrac{1}{2x})^2 = 1^2\\\\\\4x^2+\dfrac{1}{4x^2}+2=1\\\\\\4x^2+\dfrac{1}{4x^2}=-1\\\\\\[/tex]
Again applying the formula:-
[tex](4x^2+\dfrac{1}{4x^2})^2=(-1)^2\\\\\\16x^4+\dfrac{1}{16x^4}+2=1\\\\\\16x^4+\dfrac{1}{16x^4}=-1[/tex]
Hence the value of the given expression will be -1
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