Germany | A Nice Math Olympiad Problem | X = ? & Y = ?
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- เผยแพร่เมื่อ 21 พ.ค. 2024
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Sir, there is an easier way. Instead of taking x into quadratic form, we could make root(x)-root(y) by using a-b whole squared formula. After squaring root(x)+root(y) and getting the value of x+y, we see the squared expression and then subtract 4 times root (xy) to get x+y-2root(xy). This can then be brought into root(x)-root(y) form. Multiplying root(x)-root(y) with root(x)+root(y) will give us x-y. Ten after adding x+y and x-y equations, we can get x and y more easily....
Nice one, thank you 🎉
Method 3:
This is a problem with 2 unknown variables in 2 equations.
dividing √(xy) = 10 by √x leads to √y = 10/√x
replacing √y in the first equation leads to √x + 10/√x = 10
√x + 10/√x = 10 can be solved in following way:
multiplying this with√x leads to x + 10 = 10√x. By squaring both sides you find
x² - 80x + 100 = 0 with the solutions 40 + /- 10√15
@@ichdu6710 Nice one 🎉