Math Is Fun Forum

Abbey78336

Member

Registered: 2022-08-15

Posts: 37

Help me solve this. 98% of mathematicians failed

2x^2 + (432/49x) = 3

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Help me solve this. 98% of mathematicians failed

hi Abbey78336

You have already posted this here:

http://www.mathisfunforum.com/viewtopic.php?id=27863

Where did you get it from?  98% ?  I find this hard to believe as solving quadratics is something mathematicians would learn at an intermediate level and the internet has plenty of quadratic solvers.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Abbey78336

Member

Registered: 2022-08-15

Posts: 37

Re: Help me solve this. 98% of mathematicians failed

Then solve it step by step

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Help me solve this. 98% of mathematicians failed

This quadratic does not have an easy factorisable form, so it is necessary to use either the quadratic formula or the method of completing the square.  I will round off 8.81632653061224 to 8.8 to simplfy the write up but use the more accurate form for the actual calculation.

divide by 2

I have added (4.4/2)^2 and subtracted it again.

This gives (to 4dp) 0.3174 and - 4.7256 using the more accurate value for 432/49

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Phrzby Phil

Member

From: Richmond, VA

Registered: 2022-03-29

Posts: 50

Re: Help me solve this. 98% of mathematicians failed

I am thinking the equation as posted was intended for the 49x to be in the denominator, but was mis-written - should have therefore been written as (49x).

If that is the case, then it becomes a cubic equation.

I graphed the cubic for an approximation to its one real root.

---

World Peace Thru Frisbee

Abbey78336

Member

Registered: 2022-08-15

Posts: 37

Re: Help me solve this. 98% of mathematicians failed

Sorry I made a mistake it was supposed to be  2x^3 +(432/(49x)) =3

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Help me solve this. 98% of mathematicians failed

That makes more sense.

According to WolframAlpha https://www.wolframalpha.com/input?i=so … x%29+%3D+3

there are no real solutions.

Consider the graph y = 2x^3 + 432/(49x) - 3

As x tends to infinity so does y. As x tends to - infinity so does y.

There's an asymptote x = 0, with y tends to infinity from the right and - infinity from the left.

Differentiating we have

dy/dx = 6x^2 - 432/(49x^2) leading to turning points at x^4 = 72/49

So there will be a minimum just  to the right x = 1, and a matching maximum just to the left of x = -1.

Calculation shows the min is above y = 0 and the max is below.

So the graph rises up from - infinity 'tips' over at the maximium and heads off towards - infinity again.  The disconnected positive graph comes down from - infinity just after x=0, to the minimum and then up again to + infinity.

So neither section of graph crosses the x axis, confirming the 'no real solutions' statement.

To get the complex solutions without Wolfram's help may take me a little longer.  Back if I get it

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Abbey78336

Member

Registered: 2022-08-15

Posts: 37

Re: Help me solve this. 98% of mathematicians failed

What if it is 2x^2 + 432/(49x) = 3

imcute

Member

Registered: 2022-09-28

Posts: 176

Re: Help me solve this. 98% of mathematicians failed

hi Abbey78336
98%

He's attracting help,just like saying "a mathmatician is trying to solve this mysterious equation,what happens next would shock you" or "test ur iq!99.999999999% of ppl cannot complete it!"
Obviously this is bad,unethical,and maybe even a violation of forum rules(also this is not ims so this guy should not expect an answer that fast)

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Help me solve this. 98% of mathematicians failed

2x^2 + (432/49x) = 3

1. This is a game for you.

2. You are looking to see how many get it right and wrong.

3. What is this nonsense that 98% get it wrong? Are you among the 98% who get it wrong?

4. What have you done? Where's your effort?

Let me see.

2x^2 + (432/49x) = 3

2x^2 + (432/49x) - 3 = 0

The middle term can be expressed as (432/49)(x).

Use the quadratic formula. In the formula, a = 2, b = (432/49) and c = -3.

Take it from here.

Last edited by sologuitar (2022-09-29 08:05:27)