Question

Find the value of $\sqrt{12+\sqrt{12+\sqrt{12+......\infty }}}$

• A. $4$
• B. $7$
• C. $3.5$
• D. $5$

Answer 1

Answer: (A)

$4$

$y=\sqrt{12+\sqrt{12+\sqrt{}12+.......\infty }}y=\sqrt{12+y}{y}^2=12+y{y}^2-y-12=0y^2-4y+3y-12=0y(y-4)+3(y-4)=0(y+3)(y-4)=0\therefore y=-3ory=4y\ne -3asyisapositivevalue$