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ProfFrink
1 year ago

Resolving orderly is difficult in this case. Even if you normalize this equation you still have an expression like this.

Here, however, it is worth calculating the square bracket

where, fortunately, two summands are subtracted. It remains:

Here the factor r to be shortened. r=0, however, is not a solution of the original equation because a “0 is provoked by 0” division there. I did not carry out a special limit check. By further calculation, the polynomial can be reduced to the following form:

This could be FataMorgana2010 has just closed off. It would lead to quite complicated root expressions. The numerical solution leads to two real solutions

x_01 = 1,9893

x_02 = 45,082

Halbrecht
1 year ago
Reply to  Valici

You need to know what to do.

in the pension account r is a rate

What is the 4 for?

ProfFrink
1 year ago
Reply to  Valici

I don’t know. You have supplied an equation that uses the letter r as a variable. The question does not contain a reference to the ratio which should be expressed as a percentage. Maybe I would have

r_01=-1,9893

r_02=45,082

to write. These numbers solve the equation.

ProfFrink
11 months ago

If I run r in Excel to 0, then I come 250,1; so would not be a solution. This, of course, is not a clean limit calculation, just a guess.

This is a quite legitimate method to imagine. Where what the mathematicians formulate as “presumption” can already be considered as a certainty in everyday use. Yes, I also got the 250,1 limit by an Excel test. He’s right and unequal to 45100. Therefore, r=0 is not a solution.

With the cardanic formula, you could calculate the solutions exactly?

Not with the cardanic formula. This is for grade 3. Special with the solution formulas for equation 4. Here’s a wiki link.

https://de.wikipedia.org/wiki/Polynom_vierten_Grades#/media/file:Quartic_Formula.svg

Think about it. You can also calculate them exactly with a numerical method, which is arbitrary. If you need 20 decommissioning points, each numerical method also provides 20 exact decommissioning points. Instead, the solution formulas deliver a so-called exact result, almost infinitely accurate. But you get a coat of root expressions. If you want to make numbers from this, you have to start your computer again anyway. And he can only count the beautiful root expressions as exactly as his mantisse is long. Typically 10 descendants.

nobytree2
1 year ago

If it were the interest rate, r would be classic < 1 to have the classic interest rate of 1.x per 1 + r. Of course, interest rates of -198,93 and 4508,2 would also be conceivable, but untypical.

If I run r in Excel to 0, then I come 250,1; so would not be a solution. This, of course, is not a clean limit calculation, just a guess.

With the cardanic formula, you could calculate the solutions exactly?

Rammstein53
1 year ago

I guess the formula comes from the financial mathematics – and was applied incorrectly. It would be better to stop the actual task.

Halbrecht
1 year ago

I do not see anything else

It is multiplied by a gg with r^5 etc. Because of the -1 in the denominator it is possible to make nix

FataMorgana2010
1 year ago
Reply to  Halbrecht

One could first substitute x=1+r (i.e. r=x-1). Then there is only x^4 -1 in the counter, which is equal (x2 +1)(x+1)(x-1) and then (x-1) can be shortened. Then it was brought to an equation with a maximum of x^4, which can be solved theoretically.

nobytree2
1 year ago
Reply to  Halbrecht

Check out the solution of ProfFink, it splits by r and lands at r high 4, which would be detachable again (cardanic formula).

nobytree2
1 year ago
Reply to  nobytree2

Okay, I missed the answer from FataMorgana2010…