**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