Question

$Evaluate \sqrt{20+\sqrt{20+\sqrt{20+...}}}$

Answer 1

Answer:

5

Step-by-step explanation:

Let $x=\sqrt{20+\sqrt{20+\sqrt{20+...} } }$.

Then, $x^2=20+\sqrt{20+\sqrt{20+...} }$ → $x^2=20+x$

Solve $x^2-x-20=0$.

$(x+4)(x-5)=0$

∴$x=5$

$x=-4$ isn't suitable because when we say $\sqrt{n}$ when n is positive, the value is positive.