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Why I fear 6 and root

6 + √(6 + √(6 + √(6 + √(6 + √(6+............)the equation continues on. What answer do we get?How?

Note by Shaan Ragib
2 years, 6 months ago

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\(6+\sqrt { 6+\sqrt { 6+\sqrt { 6...... } } } =x\\ \quad \quad \quad \quad \quad \quad \quad 6+\sqrt { x } =x\\ \quad \quad \quad \quad \quad \quad x-\sqrt { x } -6=0\\ on\quad solving\quad we\quad get,\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad x=9\) Abu Zubair · 2 years, 6 months ago

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@Abu Zubair i assume you can solve the quadratic Abu Zubair · 2 years, 6 months ago

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@Abu Zubair how did you get √(x ) in 6+ √(x)=x? Shaan Ragib · 2 years, 6 months ago

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@Shaan Ragib look carefully the value of x

6+ sqrt(6)is repeated to infinity

so is it repeated inside the root Abu Zubair · 2 years, 6 months ago

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@Abu Zubair oh! didn't notice it the first time. thank you very much Abu Zubair Shaan Ragib · 2 years, 6 months ago

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Answer is 9 ,4 6+√(6+√(6+....... =x 6+√x =x x-√x-6=0. Solving for x x=9,4 Abu Zubair · 2 years, 6 months ago

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@Abu Zubair ummm i didn't understand. can you please explain it in words Shaan Ragib · 2 years, 6 months ago

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