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

User Andrewb
by
7.1k points

1 Answer

3 votes

Answer:

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)

User Zoltan Tirinda
by
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