Question

what is
$\sqrt{6+ \sqrt{6+ \sqrt{6 + \sqrt{6} .........$ to infinite

Answer 1

Put x=√6+√6+√6+√6.........................to infinite
Squaring both sides
x²=6+x
x²-x-6=0
x²-3x+2x-6=0
x(x-3)+2(x-3)=o
(x-3)(x+2)=0
x=3  ,  x=-2