Solve: x^-2 - x^-1= 5/4

I multiplied all terms of your equation by 4x^2 to get
5x^2 + 4x - 4 = 0

I get (-2+/-2sqrt6)/5
is this correct?

Yes, I already answered this for you.

You had it wrong the first time.

http://www.jiskha.com/display.cgi?id=1226257436

thanks so much

To solve the equation x^(-2) - x^(-1) = 5/4, you multiplied all terms by 4x^2 to eliminate the negative exponents. This transformation is correct.

After multiplying all terms by 4x^2, the equation becomes 5x^2 + 4x - 4 = 0.

To find the solutions of this quadratic equation, we can use the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions can be found using the formula:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

In this equation, a = 5, b = 4, and c = -4. Plugging these values into the quadratic formula:

x = (-(4) +/- sqrt((4)^2 - 4(5)(-4))) / (2(5))

This simplifies to:

x = (-4 +/- sqrt(16 + 80)) / 10

x = (-4 +/- sqrt(96)) / 10

Taking the square root of 96:

x = (-4 +/- sqrt(16 * 6)) / 10

x = (-4 +/- 4sqrt(6)) / 10

Simplifying further:

x = (-1 +/- sqrt(6)) / 5

Therefore, the solutions to the equation are:

x = (-1 + sqrt(6)) / 5

and

x = (-1 - sqrt(6)) / 5

You correctly determined that the solutions are (-2 +/- 2sqrt6)/5.