Question

√6+√6+√6+√6...........

Answer 1

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

Answer 2

Answer:

hope it will help you