Anyone good with math around?

[Bateleur1]

Problem with school these days, is that they solve the (primary school) equations differently to how I was taught. It means I need to “unteach” my ways and learn their ways before I can help them. The answer is the same but as many have said, it’s the steps that count.

 

BYW, thanks for the apps, as it means my wife can also assist with maths too by having the steps in front of her (yeah, I know it’s supposed to be without the s).

 

Had to go through that in anyway as we got to German as the basic math is done differently as to what we were used to in SA (the way they would write and calculate)

[TheoG]

There are always many different ways to write the steps of the same problem but luckily the first/basic principles always remains the same.

[Orbit]

Eish, where to begin.

 

1. These are equations NOT expressions - that means that to solve for x you must use inverse operations. By extension, this means that your order of operations will be reversed.

Instead of doing Brackets - Exponents - Division/multiplication - Addition/subtraction (BEDMAS) you must do Subtraction/addition - Multiplication/Division - Exponents - Brackets (SAMDEB).

 

2. The first example is a Quadratic (x^2) equation and the second a quartic (x^4) equation but they both behave the same. Since x has an even power, it will have 2 solutions (one +ve and one -ve) hence you cannot solve by "getting x on its own" and square rooting as you will "lose a solution".

 

You MUST use the method of difference of 2 squares.

ie.

x^2 - b^2 = 0      NB to get everything = 0 with a quadratic eqn. 

(x + b)(x - b) = 0

x + b = 0 Or x - b = 0

x = -b Or x = b

[Orbit]

1.

(5x^4)/3 - 20 = 0

5x^4 - 60 = 0

Divide everything by 5 and factorise

 

x^4 - 12 = 0

(x^2 - sqt12)(x^2 + sqtt12) = 0

x^2 - sqt12 = 0. OR x^2 + sqt12 = 0

Now you must factorise  the x^2 - sqt12 = 0 again

 

This is difficult to write on computer but you will essentially get x = +//12 and x = - //12

 

2. 

(3x)^2 +36^1/2 = 100

9x^2 + 6 = 100

9x^2 - 94 = 0

Now factorise

 

(3x - sqt94)(3x + sqt94) = 0

3x - sqt94 = 0 OR 3x + sqtt 94 = 0

x = (sqt93)/3. Or x = - (sqt94)/3

[mecheng89]

Eish, where to begin.

 

1. These are equations NOT expressions - that means that to solve for x you must use inverse operations. By extension, this means that your order of operations will be reversed.

Instead of doing Brackets - Exponents - Division/multiplication - Addition/subtraction (BEDMAS) you must do Subtraction/addition - Multiplication/Division - Exponents - Brackets (SAMDEB).

 

2. The first example is a Quadratic (x^2) equation and the second a quartic (x^4) equation but they both behave the same. Since x has an even power, it will have 2 solutions (one +ve and one -ve) hence you cannot solve by "getting x on its own" and square rooting as you will "lose a solution".

 

You MUST use the method of difference of 2 squares.

ie.

x^2 - b^2 = 0      NB to get everything = 0 with a quadratic eqn. 

(x + b)(x - b) = 0

x + b = 0 Or x - b = 0

x = -b Or x = b

Term I've never heard of that term. Thanks for that. 

[TheoG]

I somma call it a 4th order polynomial ... 

 

Must say up untill 1st semester 3rd year maths, I never heard the term "quartic", maybe I was not in class that day  .

 

Edit:  Googled it, I definitely missed that lesson 

Edited December 16, 2020 by Theog

[TheoG]

1.

(5x^4)/3 - 20 = 0

5x^4 - 60 = 0

Divide everything by 5 and factorise

 

x^4 - 12 = 0

(x^2 - sqt12)(x^2 + sqtt12) = 0

x^2 - sqt12 = 0. OR x^2 + sqt12 = 0

Now you must factorise  the x^2 - sqt12 = 0 again

 

This is difficult to write on computer but you will essentially get x = +//12 and x = - //12

 

2. 

(3x)^2 +36^1/2 = 100

9x^2 + 6 = 100

9x^2 - 94 = 0

Now factorise

 

(3x - sqt94)(3x + sqt94) = 0

3x - sqt94 = 0 OR 3x + sqtt 94 = 0

x = (sqt93)/3. Or x = - (sqt94)/3

 

On the first one, because there is no x^3 term, there is only 2 roots (solutions), if it did have a x^3 term, can not be solved analytically but only by a numerical method such as Newton Rapson, but sorry, thats making it way more complicated than required ...

Edited December 16, 2020 by Theog

[greys]

that's nice. I study math in college but it's not so easy task for me. Thanks to the cheap essay writer service I got good grades and saved a lot of time. These guys helped me a lot.

Edited January 15, 2021 by greys

[Slowbee]

https://www.sciencealert.com/math-genius-finally-discovers-easy-way-to-solve-quadratic-equations-after-4-000-years

 

#thefutureishere

[TheoG]

https://www.sciencealert.com/math-genius-finally-discovers-easy-way-to-solve-quadratic-equations-after-4-000-years

 

#thefutureishere

 

Very very cool, I love it !  That makes it very simple to solve quadratic equations that is not straight forward to factor.

[Slowbee]

Very very cool, I love it !  That makes it very simple to solve quadratic equations that is not straight forward to factor.

I am sure changing the school curriculum is going to be a problem - where "marks" are awarded for both steps and answer.

[TheoG]

True.  Not a problem for me though, I will just USE the method ..  

[TheoG]

Its important to note that for this new method "a = 1" is a must, if it is not, you need to divide the equation by "a" to make it "1".

 

With the old quadratic equations, matters not, "a" can be anything.

Edited January 13, 2021 by TheoG

[rudi-h]

You're trying to do too much in one step, that means you'll always make mistakes.

 

Paper and ink is cheap, write down a single step at a time.  e.g. If you have the square root of 36 in one line, repeat the whole line and just change that single term to 6.

 

Nobody gets marks for writing down fewer steps, you only get marks for the right answer

Edited January 19, 2021 by rudi-h

[TheoG]

You're trying to do too much in one step, that means you'll always make mistakes.

 

Paper and ink is cheap, write down a single step at a time.  e.g. If you have the square root of 36 in one line, repeat the whole line and just change that single term to 6.

 

Nobody gets marks for writing down fewer steps, you only get marks for the right answer

 

I think the OP was sorted long ago ...  

[rudi-h]

Maybe sorted with that one problem, but the OP will struggle as much with any other problem that might be thrown his way.

 

My advice was offered as a general pointer applicable to any future problem in any domain that the OP might face...  He did ask for direction and guidance after all

 

I think the OP was sorted long ago ...