Question

$\sqrt{5+{\sqrt{5+{\sqrt{5+........}}}}}=x$find x

• A. $$=\frac{-1+{\sqrt{21}}}{{2}}$$
• B. $$\frac{1+{\sqrt{21}}}{{2}}$$
• C. $$\frac{1-{\sqrt{21}}}{{2}}$$
• D. $$\frac{1+{\sqrt{5}}}{{2}}$$

Answer 1

Answer:

$$\frac{1+{\sqrt{21}}}{{2}}$$

If $\sqrt{5+{\sqrt{5+{\sqrt{5+........}}}}}=x$

$x=\frac{1+\sqrt{4\times5+1}}{2}$

$=\frac{1+{\sqrt{21}}}{{2}}$

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

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