Solving a Golden Radical Equation

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Комментарии
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Nice! The solution is 1/golden ratio, so i call this a reciprocal golden equation 😃💯

yoav
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It is the reciprocal of the golden ratio

georgesdermesropian
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It must be checked that x = (sqrt{5)-1)/2 is a solution. Let
F(x) := sqrt(2-sqrt(x+2))-x, for 0 <= x <= 2. Hence,
2 <= x+2 <= 4. Thus, sqrt(x+2) is real and sqrt(x+2) <= 2.
Therefore, F is a real, continuous function.
F(0) = sqrt(2 - sqrt(2))> 0 and F(2) = -2 < 0. Therefore F has
at least one zero. Since the video shows that
x = (sqrt(5)-1)/2 is the only possible zero, it must be a zero
of F and thus solve the given equation.

someperson
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How is the best way to improve logic and reasoning skills?

luygvkz