Question 10

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

Solution

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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
Answer is option C.

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