Question 10

# Find the value of $$\sqrt{552+\sqrt{552+}\sqrt{552+...}}$$

Solution

x = $$\sqrt{552+\sqrt{552+}\sqrt{552+...}}$$
$$x^2-552$$ = $$\sqrt{552+\sqrt{552+}\sqrt{552+...}}$$
$$x^2 - x - 552 = 0$$
(x-24)(x+23) = 0
x cannot be negative. Therefore, $$\sqrt{552+\sqrt{552+}\sqrt{552+...}}$$ = 24