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Question Number 106906 by Study last updated on 07/Aug/20

Answered by JDamian last updated on 07/Aug/20

$$3$$

Answered by Dwaipayan Shikari last updated on 07/Aug/20

$$\sqrt{20+\sqrt{20+\sqrt{20}}..{.}_{}}=a$$$$20+a=a^2$$$$a^2-a-20=0$$$$a=5$$$$\sqrt{12+\sqrt{12+\sqrt{12}}.}=p$$$$12+p=p^2$$$$p^2-p-12=0$$$$p=4$$$$\sqrt{6+\sqrt{6+\sqrt{6}}}=t$$$$6+t=t^2$$$$t^2-t-6=0$$$$t=3$$$$\frac{a+p}{t}=3$$

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