Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**Abbey78336****Member**- Registered: 2022-08-15
- Posts: 37

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

Offline

**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,544

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

Offline

**Abbey78336****Member**- Registered: 2022-08-15
- Posts: 37

Then solve it step by step

Offline

**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,544

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

Offline

**Phrzby Phil****Member**- From: Richmond, VA
- Registered: 2022-03-29
- Posts: 47

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

Offline

**Abbey78336****Member**- Registered: 2022-08-15
- Posts: 37

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

Offline

**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,544

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

Offline

**Abbey78336****Member**- Registered: 2022-08-15
- Posts: 37

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

Offline

**imcute****Member**- Registered: 2022-09-28
- Posts: 176

Bob wrote:

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)

Offline

**sologuitar****Member**- Registered: 2022-09-19
- Posts: 467

Abbey78336 wrote:

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)*

Offline