Only 2% correctly figured out this math question

We are given x plus y is 20 and xy is 34, and we need to find the values of x and y. There are multiple ways to solve this question, like we can make y as 20 minus x, then substitute y in here to get this quadratic equation and solve it. Or maybe we can use x minus y whole square equals x plus y whole square minus 4 times xy formula to find x minus y, and then solve a simple system of linear equation to find the value of x and y. But today, the method I am going to show you is somewhat out of the box, super fast, and generally people don't think of it, and we will do it with the help of symmetric identity. If you observe closely, this problem is symmetric in x and y, because x and y play interchangeable roles. So if you write y plus x equals 20 and yx equals 34, the problem still remains the same. Now in order to use this fact for solving the problem, we take this value 20, which is x plus y, and divide it by 2 to get 10. Now put x as 10 plus r and y as 10 minus r. This symmetrical setup makes the algebra super clean and easy to work with. Now simply put x and y into the product formula to get 10 plus r times 10 minus r equals 34. Using the standard identity a plus b times a minus b equals a square minus b square, this becomes 10 square minus r square, which is 100 minus r square, and this equals 34. Now take r square here, and 34 here to get 100 minus 34 equals r square. This gives us 66. So r square is 66. Taking the square root of both sides, we get r equals plus root 66 or minus root 66. So x equals 10 plus root 66 and y equals 10 minus root 66. And for this value of r, we get x equals 10 minus root 66 and y equals 10 plus root 66. And that's it. This was so cool. Thank you for watching.