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Can this equation be solved for F?
F/3500 = [85+(1750/F)^2)^-.5] + [74+(1750/F)^2)^-.5]
Just to be clear, this equation is read:
(F divided by 3500) equals (85 plus (1750 divided by F) squared) all to the negative one half plus (74 plus (1750 divided by F) squared) all to the negative one half.
Sorry I don't know latex.
...And for your own sake do not try to solve this equation. I am 99% sure it cannot be done unless it involves a computer program and/or imaginary numbers.
I am just hoping someone can tell me if it can or cannot be solved and why.
Noting that 3500= 2(1750), I would first simplify the notation by letting so that the equation becomes
And, to get rid of the negative exponents, I would multiply both sides by the bracketed quantities: if , then . Here, that gives .
Now, if you square both sides you will get rid of the square roots on the left but, because the square of a sum involves a "cross term", you will still have a square root on the right:
What you can do is move all except that "middle term", still involving square roots, to the left side of the equation and then square again. The good news is that you have now removed all square roots and have a polynomial equation. The bad news is that that polynomial equation will have degree 12!