Question 25

Find the value of $$\ \sqrt{30+\sqrt{30}+...}$$

Solution

Let X=$$ \sqrt{30+\sqrt{30}+...}$$

Above equation can be written as

X=$$\Rightarrow\sqrt{30+X}$$

Squaring on both sides

$$X^{2}$$=30+X

$$X^{2}$$-X-30=0

$$X^{2}$$-6X+5X-30=0

X(X-6)+5(X-6)=0

(X-6)(X+5)=0

X=-5,6

Taking positive value

X=6

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