Question

$\sqrt{27+\sqrt{27+\sqrt{27+..........}}}=?$

• A. 3
• B. $$\frac{1+\sqrt{4\times27}}{2}$$
• C. $$\frac{1-\sqrt{4\times27}}{2}$$
• D. 12

Answer 1

Answer:

$$\frac{1+\sqrt{4\times27}}{2}$$

$\sqrt{27+\sqrt{27+\sqrt{27+..........}}}$

$=\frac{1+\sqrt{4\times27}}{2}$

$\because \sqrt{a+{\sqrt{a+{\sqrt{a+........}}}}}=x$

then${x}=\frac{1+\sqrt{4\times{a}+1}}{2}$