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 \;answerkeywords
root 5 root 5 root 5 upto infinity