Question

If (x/100-1)(x/100+1)=kx^2-1, k=

Answer 1

k=
`(1)/(10000)`

Explanation:

The given equation to us is

`((x)/(100)-1)((x)/(100)+1)=kx^(2)-1`

Now the RHS of the equation can be written as

(a-b)(a+b) = a²-b²

So the given equation becomes

`((x)/(100))^(2)-(1)^(2)=kx^(2)-1`

Squaring the terms which have square over them

`(x^(2) )/(100^(2))-1=kx^(2)-1`

as 100² = 10000 so putting its value

`(x^(2) )/(10000)-1=kx^(2)-1`

Adding one on both sides of the equation

`(x^(2) )/(10000)-1 + 1=kx^(2)-1+1`

it becomes

`(x^(2) )/(10000)=kx^(2)`

Now to get the value of K we have to divide both side of the equation with x²

so dividing with x² gives

`(x^(2) )/(10000 * x^(2) ) =(kx^(2) )/(x^(2) )`

Cutting out the same terms gives us

`(1)/(10000) =(k)/(1)`

or

k=
`(1)/(10000)`