Solve this.... with steps and explain me the answer
x=root(4+root(4-root(4+root(4-.....)
solve this ...
Refer comment

Question

anonymous · Answer

$$\sqrt{4+\sqrt{4-\sqrt{4+\sqrt{4.......}}}}$$

ganeshie8 · Answer

square both sides

ganeshie8 · Answer

$$\rm x = \sqrt{4+\sqrt{4-\sqrt{4+\sqrt{4-\cdots}}}}$$

ganeshie8 · Answer

$$\rm x^2-4 = \sqrt{4-\sqrt{4+\sqrt{4-\cdots}}}$$

ganeshie8 · Answer

square again

ganeshie8 · Answer

$$\rm \left(x^2-4\right)^2  = 4 - \sqrt{4+\sqrt{4-\cdots}}$$

ganeshie8 · Answer

Notice that infinite nexted radical on right hand side is just x

anonymous · Answer

the problem what I am facing is solving the 4th degree equation!

ganeshie8 · Answer

$$\rm \left(x^2-4\right)^2  = 4 - x$$

solve x such that  $x \ge 0$ and $x^2 - 4 \ge 0$

anonymous · Answer

i had already derives the equation till the step you have shown

ganeshie8 · Answer

ganeshie8 · Answer

solving 4th degree eqn is indeed a pain

anonymous · Answer

isnt there a shorter method to calculate manually

ganeshie8 · Answer

you can work it by hand by factorizing it into two quadratics, but i don't think it is easy

anonymous · Answer

chalo thanks..!

ganeshie8 · Answer