More Math Questions I can't figure out, from a practice test.

Question

1. The difference between 2 positive numbers is 4√3. The product of the 2 numbers is 4. What is the absolute value of the difference of their reciprocals?
2. For what values does the √2x equal x√2?
3. 3 children played a game; two won and one lost on play. The loser had to double the points of each winner by subtracting from his or her own points. They played the game 3 times, each winning twice and losing once, At the end, each had forty points. How many points did each have to start?

It would be great if you could show me how to solve these using algebra. Thanks!

Answer 1

x - y = 4sqr3,

xy = 4

substitute into right side of 1st equation

x-y = xysqr3

divide both sides by xy

x/xy - y/xy = sqr3

simplify the left side

1/y - 1/x = sqr3

|1/y - 1/x| = |1/x - 1/y| = sqr3 = about 1.732

absolute value of the difference of the reciprocals = the positive square root of 3