Answer:
k=[tex]\frac{1}{10000}[/tex]
Step-by-step explanation:
The given equation to us is
[tex](\frac{x}{100}-1)(\frac{x}{100}+1)=kx^{2}-1[/tex]
Now the RHS of the equation can be written as
(a-b)(a+b) = a²-b²
So the given equation becomes
[tex](\frac{x}{100})^{2}-(1)^{2}=kx^{2}-1[/tex]
Squaring the terms which have square over them
[tex]\frac{x^{2} }{100^{2}}-1=kx^{2}-1[/tex]
as 100² = 10000 so putting its value
[tex]\frac{x^{2} }{10000}-1=kx^{2}-1[/tex]
Adding one on both sides of the equation
[tex]\frac{x^{2} }{10000}-1 + 1=kx^{2}-1+1[/tex]
it becomes
[tex]\frac{x^{2} }{10000}=kx^{2}[/tex]
Now to get the value of K we have to divide both side of the equation with x²
so dividing with x² gives
[tex]\frac{x^{2} }{10000 * x^{2} } =\frac{kx^{2} }{x^{2} }[/tex]
Cutting out the same terms gives us
[tex]\frac{1}{10000} =\frac{k}{1}[/tex]
or
k=[tex]\frac{1}{10000}[/tex]
