Math Olympiad | Can you solve this ? | A Nice Algebra Equation with Square Roots

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[@Yureka-ox5jn]

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[@learncommunolizer]

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[@is7728]

What an excellent question and method

[@learncommunolizer]

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[@zvonimirkujundzic6867]

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[@roger7341]

Let y=2+√3 and 1/y=2-√3. Let z=y^x, giving z+1/z-4=0 or z^2-4z+1=0, which has roots z=(4±2√3)/2=2±√3
From z=y^x=2±√3=(2+√3)^x it follows that x=±1, which is easily verified by substituting x=±1 into the given equation.

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[@learncommunolizer]

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[@user-lf5jt2hu7j]

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[@spelleg11]

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[@learncommunolizer]

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[@user-ec5ip3vp2r]

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