An algebra problem....

[MrFrog]

TFS. free time ekaka balanna ona.

 

[Ozone4]

@AnuradhaRa පොඩි උන්ට ගනන් ඉගැන්නුව නේද කියන්න බලන්න උත්තරේ

Dan itin oka awith Thread 1k daai, "Me gana hadaganna mage Account 1ta kiyak Hari Daanna" Kiyala..

 

[NRTG]

කොහොමද මචං එහෙම 0 ට සමානයි කියල ගන්නෙ?

මට ආව උත්තරේ තමයි මචන් ඔය උඩ මම දාලා තියෙන්නේ ....

 

[AVES]

When x -> ±∞, y -> 0 &
y -> ±∞, x -> 0 at the same time. Isn't it?

 

[kinkon]

 

[hodakolla]

BUMPER

ekak ma dannam ganan hadanna ba

 

[Ramiel]

BUMPER

ekak ma dannam ganan hadanna ba

මහත්තයා ලීසින් කරන්නෙ ගනන් බැරුවද? HNB එකට දෙයියන්ගෙම පිහිටයි

 

[hodakolla]

මහත්තයා ලීසින් කරන්නෙ ගනන් බැරුවද? HNB එකට දෙයියන්ගෙම පිහිටයි

E ganan wage neme aiye me ganan hrima amrui ekai

 

[EKGuest]

For those who are interested....

Find the whole number solutions for the following equation.

View attachment 150893

I couldn't solve this problem but we can write code to find some of the answers for x and y.

using System;

internal class Program
{
    static void Main(string[] args)
    {
        long rangeMax = 10000;
        long rangeMin = -rangeMax;

        for (long x = rangeMin; x <= rangeMax; x++)
        {
            for (long y = rangeMin; y <= rangeMax; y++)
            {
                if (  (x * x) + (4 * y * y) == ( (x * y - 14) * (x * y - 14) )  )
                {
                    Console.WriteLine("x = {0}\ty={1}", x, y);
                }
            }
        }

        Console.ReadLine();
    }
}

Note that above output doesn't prove those are the only answers for x and y. It simply shows the answers for x and y within the seleted range, (-10,000 to 10,000)

 

[imhotep]

I couldn't solve this problem but we can write code to find some of the answers for x and y.

using System;

internal class Program
{
    static void Main(string[] args)
    {
        long rangeMax = 10000;
        long rangeMin = -rangeMax;

        for (long x = rangeMin; x <= rangeMax; x++)
        {
            for (long y = rangeMin; y <= rangeMax; y++)
            {
                if (  (x * x) + (4 * y * y) == ( (x * y - 14) * (x * y - 14) )  )
                {
                    Console.WriteLine("x = {0}\ty={1}", x, y);
                }
            }
        }

        Console.ReadLine();
    }
}

View attachment 192441

Note that above output doesn't prove those are the only answers for x and y. It simply shows the answers for x and y within the seleted range, (-10,000 to 10,000)

Good effort.. Thanks...!!!
It's over an year since I posted it and I forgot to post the solution as well. Yes... these two are the Integer solutions to the problem, other than the trivial integer solution x=0, y = ± 7 and y=0, x = ± 14

By rearranging it you can solve it algebraically for a generalized solution

y = (14x - SQR(x^4 - 4x^2 + 784))/ (x^2 - 4) when X^2 is not equal to 4
y= ((SQR(x^4 - 4x^2 + 784) + 14x))/(x^2 - 4) when x^2 is not equal to 4

When x^2 is equal to 4 then.
when x = 2 , y = 24/7 also when x = -2 , y = -24/7

 

[Ryan08]

Bump

 

[Candid-B]

X^2+4xy+4y^2 = xy^2-28x+196
@AnuradaRa අනුරාධ රාමනුජන්ට බැරි වුණා නම් අපිටත් බෑ.

 

[eksudda]

Bump

 

[07sanjeewakaru]

I couldn't solve this problem but we can write code to find some of the answers for x and y.

using System;

internal class Program
{
    static void Main(string[] args)
    {
        long rangeMax = 10000;
        long rangeMin = -rangeMax;

        for (long x = rangeMin; x <= rangeMax; x++)
        {
            for (long y = rangeMin; y <= rangeMax; y++)
            {
                if (  (x * x) + (4 * y * y) == ( (x * y - 14) * (x * y - 14) )  )
                {
                    Console.WriteLine("x = {0}\ty={1}", x, y);
                }
            }
        }

        Console.ReadLine();
    }
}

View attachment 192441

Note that above output doesn't prove those are the only answers for x and y. It simply shows the answers for x and y within the seleted range, (-10,000 to 10,000)

These are the only solutions......

------ Post added on Dec 23, 2022 at 2:53 PM

 

[imhotep]

Thanks for @EKGuest & @07sanjeewakaru for responding and finding a solution even after a year, when I had already forgotten about it.

 

[07sanjeewakaru]

Thanks for @EKGuest & @07sanjeewakaru for responding and finding a solution even after a year, when I had already forgotten about it.

Wonderful problem....

 

[DHE]

BUMP