x^-2 - x^-1 - 20 = 0?

Question

what is the answer to this? is it 0=20 which of course 0 doesn't = 20.

Answer 1

1/x^2 - 1/x - 20 = 0

To solve this problem, you need to get a little creative with algebraic transformation - in essense, convert the fraction into something easier to solve. In this case, you can convert to a quadratic equation.

1.) Multiply everything to get a common denominator. In this case, use x^2 as the denominator, to get a quadratic equation in the nominator.
1/x^2 - 1/x * x/x - 20 * x^2/x^2 = 0
(1 - x - 20x^2)/x^2 = 0

2.) Multiply both sides by x^2 to leave you with the quadratic equation.
(1 - x - 20x^2)/x^2 = 0
(1 - x - 20x^2)/x^2 = 0
1 - x - 20x^2 = 0

3.) Rewrite the formula to express as a classic quadratic equation:
-20x^2 - x + 1 = 0

4.) Use the quadratic formula:
x = (-b +/- (b^2 - 4ac) ^1/2)/2a
x = (1 +/- (1 - (4 * -20 * 1))^1/2)/-40
x = (1 +/- (81)^1/2)/-40
x = (1 + 9)/-40 , (1 - 9)/-40
x = -1/4, 1/5 (solutions)

Check:
1/(-1/4)^2 - 1/(-1/4) - 20 = 0
1/(1/16) - 1/(-1/4) - 20 = 0
16 + 4 - 20 = 0 (correct!)

1/(1/5)^2 - 1/(1/5) - 20 = 0
1/(1/25) - 1/(1/5) - 20 = 0
25 - 5 - 20 = 0 (correct!)

Answer 2

x^-2 - x^-1 - 20 = 1/x^2 - 1/x - 20 = 0
Multiply through the equation by x^2 which is the LCD
This gives
1 - x - 20x^2 = 0 or
20x^2 + x - 1 = 0

Factor the left side and you get

(4x + 1)(5x - 1) = 0

x = -1/4 , 1/5

Note: x cannot = 0 in the first place since this would cause a division by 0 which is undefined.

Answer 3

? ... there is already an answer in your question.. It is 0
or if your finding the other numbers Look at this..If you have an equation using multiplication and you have the product as a given, divide it to the right to get the answer..