Math, asked by sandossh, 1 year ago

√6+√6+√6+√6...........

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Answered by Mathexpert

Let x = $\sqrt{6+ \sqrt{6+ \sqrt{6+} \sqrt{6+........} } }$

Squaring on both sides

x² = 6 + $\sqrt{6+ \sqrt{6+ \sqrt{6+} \sqrt{6+........} } }$

⇒x² = 6 + x

⇒ x² - x - 6 = 0

⇒ (x-3)(x+2) = 0

⇒ x = 3 or x = -2

Ignoring negative value,,

x = 3

⇒ $\sqrt{6+ \sqrt{6+ \sqrt{6+} \sqrt{6+........} } }$ = 3

sandossh: sir how x2=6+x

Mathexpert: As the term √6+√6+√6+√6........... is an infinite term....so after squaring on both sides...it remains 6 + √6+√6+√6+√6...............so it is 6 + x on RHS

sandossh: Thnx expert..please answer my other question

Answered by sam4915

Answer:

hope it will help you

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