SOLUTION: How do you solve x^-1 - x^-2 = 3/4 I tried the u substitution but did not get the correct answer. I keep getting -1/2 plus or minus i radical 2 over two But the answer I nee

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How do you solve x^-1 - x^-2 = 3/4 I tried the u substitution but did not get the correct answer. I keep getting -1/2 plus or minus i radical 2 over two But the answer I nee      Log On


   

Question 736540: How do you solve
x^-1 - x^-2 = 3/4
I tried the u substitution but did not get the correct answer. I keep getting -1/2 plus or minus i radical 2 over two
But the answer I need to get to is -2,2/3
Please help!
Found 2 solutions by josgarithmetic, htmentor:
Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
EDIT(small arithmetic mistake correction):
Realize your equation is the same as 1%2Fx%2B1%2F%28x%5E2%29=3%2F4. LCD is 4x%5E2, so multiply left and right members by 4x%5E2. You should obtain this:

4x-4=3x%5E2.

If you have that within your solution steps, you were doing well up to such point.

Simplifies further to 3x%5E2-4x%2B4=0,
factorable into ---No. NOT factorable.
Use formula for solution to a quadratic equation. It will simplify to
highlight%28x=2%2F3-i%282%2F3%29sqrt%282%29%29 or highlight%28x=2%2F3%2Bi%282%2F3%29sqrt%282%29%29

The expected -2 or 2/3 is incorrect.

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
How do you solve
x^-1 - x^-2 = 3/4
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I think you have a typo. Should that be x^-1 - x^-2 = (-)3/4 ???
Otherwise there are no real solutions, as you found.
To solve move -3/4 to the LHS of the equation and multiply through by x^2:
(3/4)x^2 + x - 1 = 0 -> x^2 + 4/3x - 4/3 = 0
We can cleverly factor this (knowing the answer ahead of time helps ;-)) as:
(x+2)(x-2/3) = 0
Now we can read off the answers x=-2, x=2/3