Exponential equation | How To Solve Diophantine Equations | Diophantine Equations.

Diophantine equations are some times rhetorical to solve analytically due to the tough nature of some of them the graphical method is best applied in solving them.
In this video "How To Solve The Diophantine Equation, 3^x+x^2=5", I will guide you systematically through the applications of some mathematical laws in order to solve this tough challenge with easy.
For the full details, watch from the beginning to the end without skipping any parts.
Kindly leave a comment bellow for a better approach if any in the comment section.

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[arbab]

I love your way of solving such problems. Good luck. This is really genious.

[maxwellarregui]

Sres. OnlineMath TV reciban un cordial saludo, gracias este interesante ejercicio, al ser una ecuación de segundo grado, sería dos raíces x1 = 1.17238462 y x2 = -2.21639312. éxitos.

[wirtumromzyreigns]

Good solving Sir
But from equation (2) you can look for the value of X, i.e from 3⁰=5^½-x, →x=1.236
when I substitute x=1.236 in the initial eqn it gives me 5.415...≈5

[Yes_I_cn]

But isn't that the same as saying, for instance, that 12 x 1 = 4 x 3 and then saying that 12 = 4 and 1 = 3? This is obvioulsy not true. I am confused then...

[normb]

Hi. Thank you for your very interesting videos. I have one question. Since there is an x^2 in the equation, should there be 2 solutions? When I used Mathway to solve this equation, it came up with 2 values for x. x ≈ −2.21639311, and 1.17238462. Also, @luisgoncalves raised a question that I find myself asking. Thanks very much.

[yuhani]

thank you very much, it's beautiful

[tontonbeber]

Yes, but that's not a Diophantine Equation.
By definition, a Diophantine Equations is when solutions are integers.

[RudySchmidt-ic]

Your equation 2 is 3^0=5^(1/2)- x
So we can use this equation only to solve for x.
X=5^(1÷2)-3^0=1.2361

[ericklira]

Por graficas de la exponencial y la cuadratica hay dos soluciones reales

[bobwineland]

Could you please give a formal proof that 3^X =(5^1/2+X) and 3^0=(5^1/2-X) as pertains to your example? If a times b = c times d, it
doesn't necessarily follow that a=c.

[syedmdabid]

The caliculator isn't allowed in the EXAM. Why did u?

[chuksnonso]

Some of the assumptions not clear to me

[oleglevchenko]

In the title, you mention 'Diophantine equation' three times!
Wikipedia: "a Diophantine equation is an equation, ... such that the only solutions of interest are the integer ones"
I doubt your solution is integer...

[samimarzou]

I lost you at 5:30 when you added both equations (i) and (ii) as if they were independent

[stefangaudes]

Unfortunately, this time it doesn't work with a simple equation from the product of the quadratic equation. The result obtained in this way is somewhat too small. Try again with the approach x1 = x0 - f(x0)/f'(x0). The numerical result is approximately 1.17238462

[axwazou]

excuse me you are wrong the true solutions are : x1 = -2.21, x2= 1.17 . every one can test