Question

If x = root 5 + root 5 + root 5 till infinity and X is a natural number form a quadratic equation

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$\displaystyle{\rightarrow x^2-x-5=0}$

Step-by-step explanation:

Given :

$\displaystyle{x=\sqrt{5+\sqrt{5+\sqrt{5+ \ .. \ to \ \infty}}}}$

Now :

$\displaystyle{x=\sqrt{5+\sqrt{5+\sqrt{5+ \ .. \ to \ \infty}}}}\\\\\\\displaystyle{x=\sqrt{5+x}}$

Squaring on both side :

$\displaystyle{\rightarrow x^2=(\sqrt{5+x}})^2\\\\\\\displaystyle{\rightarrow x^2=x+5}\\\\\\\displaystyle{\rightarrow x^2-x-5=0}$