Question

The value of $\sqrt{8+2\sqrt{8+2\sqrt{8+......}}}$

• A. $8$
• B. $10$
• C. $11$
• D. $4$

Answer 1

The correct option is D $4$

$y=\sqrt{8+2\sqrt{8+2\sqrt{8+\dots }}}$

$y=\sqrt{8+2y}$

$y^2=8+2y$

$y^2-2y-8=0$

$y^2-4y+2y-8=0$

$y(y-4)+2(y-4)=0$

$(y+2)(y-4)=0$

$y=-2$ or $4$