# Why I fear 6 and root

6 + √(6 + √(6 + √(6 + √(6 + √(6+............)the equation continues on. What answer do we get?How?

Note by Shaan Ragib
3 years, 5 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

$$6+\sqrt { 6+\sqrt { 6+\sqrt { 6...... } } } =x\\ \quad \quad \quad \quad \quad \quad \quad 6+\sqrt { x } =x\\ \quad \quad \quad \quad \quad \quad x-\sqrt { x } -6=0\\ on\quad solving\quad we\quad get,\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad x=9$$

- 3 years, 5 months ago

i assume you can solve the quadratic

- 3 years, 5 months ago

how did you get √(x ) in 6+ √(x)=x?

- 3 years, 5 months ago

look carefully the value of x

6+ sqrt(6)is repeated to infinity

so is it repeated inside the root

- 3 years, 5 months ago

oh! didn't notice it the first time. thank you very much Abu Zubair

- 3 years, 5 months ago

Answer is 9 ,4 6+√(6+√(6+....... =x 6+√x =x x-√x-6=0. Solving for x x=9,4

- 3 years, 5 months ago

ummm i didn't understand. can you please explain it in words

- 3 years, 5 months ago