Question

$\sqrt{20 + \sqrt{20 - \sqrt{20 + \sqrt{20 - \sqrt{20.... \infty } } } } }$

Answer 1

Heya user,
_____________________________________________________________


Let x = √(20 + √(20 - √(20 + .......
Then, x²  - 20 = √(20 - √(20 + ......
=> [ x² - 20 ]² - 20 = -x
=> [ x⁴ - 40x² + x - 380 = 0 ]
=> x has 4 real values --> [ 1 + √77 ]/2 ; [ 1 - √77 ]/2 ; [ 39 plus minus √1601 ]/2 
_____________________________☺______________________________