×

# 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
1 year, 9 months ago

Sort by:

$$6+\sqrt { 6+\sqrt { 6+\sqrt { 6...... } } } =x\\ \quad \quad \quad \quad \quad \quad \quad 6+\sqrt { x } =x\\ \quad \quad \quad \quad \quad \quad x-\sqrt { x } -6=0\\ on\quad solving\quad we\quad get,\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad x=9$$ · 1 year, 9 months ago

i assume you can solve the quadratic · 1 year, 9 months ago

how did you get √(x ) in 6+ √(x)=x? · 1 year, 9 months ago

look carefully the value of x

6+ sqrt(6)is repeated to infinity

so is it repeated inside the root · 1 year, 9 months ago

oh! didn't notice it the first time. thank you very much Abu Zubair · 1 year, 9 months ago

Answer is 9 ,4 6+√(6+√(6+....... =x 6+√x =x x-√x-6=0. Solving for x x=9,4 · 1 year, 9 months ago