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**meerblau****Member**- Registered: 2016-02-17
- Posts: 3

My math classes are toooo long ago. Any help to sove this? :-)

f(z) = 4z4-3z3+15z2-9

f(y) = 7y4+38y3+7y2-200

f’(y) = 29772

f’(z) = -1+873y

*Last edited by meerblau (2016-02-17 05:38:36)*

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**meerblau****Member**- Registered: 2016-02-17
- Posts: 3

Sorry, I edited the post.

I would like to know what z is.

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Did this question come with any other information?

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**Grantingriver****Member**- Registered: 2016-02-01
- Posts: 105

f(z) = 4z⁴-3z3³+15z²-9. → 1

f(y) = 7y⁴+38y³+7y²-200 → 2

f’(y) = 29772 → 3

f’(z) = -1+873y → 4

From the first and the second equations we have:

f'(z)=16z3³-9z²+30z and f'(y)=28y³+114y2²+14y hence:

2(14y³+57y²+7y)=29772 ⇒ 14y³+57y²+7y= 14886 ⇒ y=9, y≈-6.5+8.7i and y≈-6.5-8.7i

If you seek the real solution then we use the first real answer which is "y=9" in the forth equation so we have:

16z³-9z²+30z=-1+873×9 ⇒ 16z³-9z²+30z=7856 ⇒ z=8, z≈6.9+3.7i and z≈-6.9+3.7i.

Now since it is obvious that you need the real roots (since they are the required values in many applications), therefore the solutions are "y=9 and z=8".

Note: you can find other solutions by substituting the complex roots of y in the forth equation.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

That looks right, sorry for the confusion caused by my answer. I have deleted it.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**meerblau****Member**- Registered: 2016-02-17
- Posts: 3

Thank you so much for your help! Now I wonder even more that I was able to sollte that during my school days ;-).

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