how to solve infinite root 5 problems | infinite square root of 5| how to solve infinite nested radicals

Share

how to solve infinite root 5 problems and solutions

x=\sqrt{5-\sqrt{5-\sqrt{5-\sqrt{5-\sqrt{5-...}}}}}

 Squaring both sides, we get 

x^2=5-\sqrt{5-\sqrt{5-\sqrt{5-\sqrt{5-\sqrt{5-...}}}}}
x^2=5-x\\ \\ x^2+x-5=0

solve this using the quadratic formula.

a=1\; , b=1 ,\;c=-5
x=\frac{-b\;\pm \sqrt{b^2-4ac}}{2a}
x=\frac{(-1)\;\pm \sqrt{1-4(-5)}}{2}
=\frac{-1\pm \sqrt{21}}{2}

Remember, positive square roots x is a square root and thus a positive square root

so x\geq 0

only\;x=\frac{-1+ \sqrt{21}}{2} \;\;is \;valid \;answer

keywords

root 5 root 5 root 5 upto infinity


Share
Related  बौधायन त्रिकोणमितीय फलन Baudhayan Trigonometric Function TRIGONOMETRY DEVELOPMENT IN ANCIENT

Leave a Reply

Your email address will not be published. Required fields are marked *

Top 5 Most Expensive Domains Ever Sold 4 Must-Try ChatGPT Alternatives: Perplexity AI, BardAI, Pi, and More! Types of Trading Techniques in the Stock Market. ChatGPT app now available in India this AI chatbot can help you make your life more productive. What is wrong with following function code?