Question

$\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + ..........} } } } } }$
find the value of above ?​

Answer 1

Answer:

The Answer is 2.99993

.............................................

Answer 2

let x=

$\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6.. \infty } } } }$

on squaring both side

${x}^{2} = 6 + \sqrt{6 + \sqrt{6 + \sqrt{6} } }$

x²=6+x

x²-x-6=0

$x = 1 + - \sqrt{25 } \div 2 \\( 1 + - 5) \div 2$

x=3, -2

since negative is neglect so x=3 is appropriate answer

hope it is helpful it take too much time for written this..