1/x^2-1=1000

Solution for 1/x^2-1=1000 equation:

1/x^2-1=1000

We move all terms to the left:

1/x^2-1-(1000)=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

1/x^2-1001=0

We multiply all the terms by the denominator


-1001*x^2+1=0

We add all the numbers together, and all the variables

-1001x^2+1=0

a = -1001; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-1001)·1
Δ = 4004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4004}=\sqrt{4*1001}=\sqrt{4}*\sqrt{1001}=2\sqrt{1001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1001}}{2*-1001}=\frac{0-2\sqrt{1001}}{-2002}
=-\frac{2\sqrt{1001}}{-2002}
=-\frac{\sqrt{1001}}{-1001}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1001}}{2*-1001}=\frac{0+2\sqrt{1001}}{-2002}
=\frac{2\sqrt{1001}}{-2002}
=\frac{\sqrt{1001}}{-1001}
$