Friday, 18 January 2013

Euler Piruleta Vs. The Crazy Maths Teacher

Congratulations to all of you who have built your own Origami Twisted Tower!! :D

You are clearly THE BEST!!

If you want to download the pictures with better quality, use the links below:

Origami Twisted Tower 3ºAD
Origami Twisted Tower 3ºCD

Now that it seemed we knew everything related to equations, a new menace is plotting against the life on Earth! This time a Crazy Maths teacher has built an algebraic bomb which has the power to erase every living creature from the surface of our planet. Only a reckless hero as Euler Piruleta has the bravery to try to deactivate it... 

The problem is that he needs to get 12 codes which are the solution for some 4th degree equations to deactivate the bomb, but he only studied 2nd order equations in the high school (at this moment, he wishes his former teacher had taught him how to solve more equations, but it is too late..).

Euler needs desperately your help!! Will you help him to solve these 4th degree equations?

We have studied how to solve first and second order equations. Trying to solve a 3rd order equation with a formula may bring about the most terrible operations you have ever imagined, as long as the formulas to get the 3 solutions of an equation like $ax^{3}+bx^{2}+cx+d=0$ (where a, b, c, d are real numbers) are:

It has been proved that there is no possible formula for the general equation of degree 4, but it’s quite interesting that some 4th order equations can be solved easily transforming them into 2nd order equations. These equations are called Biquadratic Equations.

Try to solve the following biquadratic equations to get the codes Euler Piruleta needs to deactivate the bomb. Write the 12 codes you get in the chart below… is the only way of deactivating the bomb!!!

a) $x^{4}-10x^{2}+9=0$                   b) $x^{4}+3x^{2}+2=0$                       c) $4x^{4}-17x^{2}+4=0$

The Bomb’s Codes
Nº 1
Nº 2
Nº 3
Nº 4
Nº 5
Nº 6
Nº 7
Nº 8
Nº 9
Nº 10
Nº 11
Nº 12

Note: if one code is not a real number, you must enter #.

The instructions to solve these equations can be downloaded here! C'mon, it shouldn't take you any longer than 15 minutes to help poor Euler Piruleta! :D

Deadline: January the 25th. You can either send me an e-mail with the 12 codes or give a handwritten copy next week :) 


- Juan has been the winner of the Euler Piruleta's Face contest!! Therefore, he has been awarded with 2 challenge positives!

- Belén, Carlos and Iñaki have been incredible runner-ups, so they have been awarded with 1 challenge positive!

- Iñaki, Jorge, Iván and Tania have a new challenge positive for the Second Order Equations Formula!

- Some music for the weekend: you should know that some of the most famous songs nowadays are versions of songs from the 80's. Here is one fine example

Pitbull feat. Christina Aguileara Vs. A-Ha

I wonder which version you prefer... :P


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