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

Note by Shaan Ragib 3 years, 5 months ago

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\(6+\sqrt { 6+\sqrt { 6+\sqrt { 6...... } } } =x\\ \quad \quad \quad \quad \quad \quad \quad 6+\sqrt { x } =x\\ \quad \quad \quad \quad \quad \quad x-\sqrt { x } -6=0\\ on\quad solving\quad we\quad get,\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad x=9\)

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i assume you can solve the quadratic

how did you get √(x ) in 6+ √(x)=x?

@Shaan Ragib – look carefully the value of x

6+ sqrt(6)is repeated to infinity

so is it repeated inside the root

@Abu Zubair – oh! didn't notice it the first time. thank you very much Abu Zubair

Answer is 9 ,4 6+√(6+√(6+....... =x 6+√x =x x-√x-6=0. Solving for x x=9,4

ummm i didn't understand. can you please explain it in words

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boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

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`[example link](https://brilliant.org)`

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`\sin \theta`

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## Comments

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TopNewest\(6+\sqrt { 6+\sqrt { 6+\sqrt { 6...... } } } =x\\ \quad \quad \quad \quad \quad \quad \quad 6+\sqrt { x } =x\\ \quad \quad \quad \quad \quad \quad x-\sqrt { x } -6=0\\ on\quad solving\quad we\quad get,\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad x=9\)

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i assume you can solve the quadratic

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how did you get √(x ) in 6+ √(x)=x?

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6+ sqrt(6)is repeated to infinity

so is it repeated inside the root

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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

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ummm i didn't understand. can you please explain it in words

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