SOLUTION: This involves negative exponents and "equations quadratic in form." The equation is: x^-4 - 10^-2 + 9 = 0 (those are negative exponents: x to the negative fourth power, etc.) To

Question 1057311: This involves negative exponents and "equations quadratic in form." The equation is:
x^-4 - 10^-2 + 9 = 0 (those are negative exponents: x to the negative fourth power, etc.)
To make solving easier, a substitution is used. Let u = x^-2, and rewrite the original equation as a quadratic equation:
u^2 - 10u + 9 = 0
Factor: (u-1)(u-9) = 0
Apply the zero-product principle: u-1 = 0 or u-9 = 0; so:
u = 1 or u = 9
Now replace u with x^-2 in each of the above equations:
x^-2 = 1 or x^-2 = 9.
Get rid of the negative exponents:
1/x^2 = 1 or 1/x^2 = 9
And now here is where I get confused. At this point, my professor writes this on the board as the next step:
x^2 = 1 or x^2 = 1/9
I have no idea how he got from the previous step to this step.
From here, he goes on to apply the square root property:
x = +-1 or x = +-1/3
This is the final answer.
So my question is:
How do we get from
1/x^2 = 1 or 1/x^2 = 9
to
x^2 = 1 or x^2 = 1/9
?
Thank you for any help you can give, and my apologies for the long question.

Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52810) (Show Source): You can put this solution on YOUR website!
.
So my question is:
How do we get from
1/x^2 = 1 or 1/x^2 = 9
to
x^2 = 1 or x^2 = 1/9
?
~~~~~~~~~~~~~~~~~~~~~~~

If = 1, then multiply both sides by , and you will get 1 = , which is the same as = 1. If = 9, then multiply both sides by , and you will get 1 = , which is the same as = 1. Now divide both sides of the last equation by 9, and you will get = .

Answer by MathTherapy(10553) (Show Source): You can put this solution on YOUR website!

How do we get from
1/x^2 = 1 or 1/x^2 = 9
to
x^2 = 1 or x^2 = 1/9
?
Thank you for any help you can give, and my apologies for the long question.

------ Cross-multiplying

Likewise, becomes:
------- Cross-multiplying
------- Dividing each side by 9

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