Solving System of Equations For Integers | Interesting Algebra Problem with Radicals

🔴Solving System of Equations For Integers | Interesting Algebra Problem with Radicals

Hello there.
Today, we are going to solve a nice algebra problem, where we are given a system of equations, and we are supposed to solve for integer values.

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topics covered in this video:
Solving System of Equation
Solve For Integer Solutions
Interesting Algebra Problem
Diophantine Equation
Radical Equation
Math Olympiad Problem

#SolveForIntegers #canYou Solve #MathOlympiadQuestion

[dhruvakhera]

I put the linear terms on one side then squared so i got the fxn of a circle which is S=x^2+y^2-23x-15y+170, S=0. 9, 4 does lie on this circle however i wouldn't have been able to figure out the integer values so i will learn this method as well, thank you for the solution :)

[richardtaylor]

Since x and y are both positive integers, y < 7 and x < 11; and since they must both be squares x is 1, 4 or 9 and y is 1 or 4. So it is quicker to try all the combinations in your head than to do any algebra here...

[jim]

By inspection x = 9 and y = 4. That said, it's informative to see how a system of equations is solved when radicals are involved.

[MyOneFiftiethOfADollar]

You will have better luck by producing your own original content. This is famous problem that has been published at hundreds if not thousands of YouTube channels. It is way too easy to guess and test. Do one with larger constants where viewer will not be able to guess the answer. Good luck