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Question Number 151174 by mathdanisur last updated on 18/Aug/21

$$\sqrt[3]{a+\sqrt{3\cdot \sqrt[3]{a+\sqrt{3\cdot \sqrt[3]{a+\sqrt{3\cdot ...}}}}}}=3$$$$\mathrm{find}a=?$$

Answered by mr W last updated on 18/Aug/21

$$\sqrt[3]{a+\sqrt{3\times 3}}=3$$$$a+3=27$$$$a=24$$

Commented by mathdanisur last updated on 18/Aug/21

$$\mathrm{Thankyou}\mathrm{Ser}$$

Answered by maged last updated on 18/Aug/21

$$let$$$$\sqrt[3]{a+\sqrt{3\cdot \sqrt[3]{a+\sqrt{3\cdot \sqrt[3]{a+\sqrt{3\cdot ...}}}}}}=u$$$$\Rightarrow u=3$$$$\sqrt[3]{a+\sqrt{3u}}=3$$$$a+\sqrt{3u}=27$$$$a+\sqrt{9}=27$$$$a=27-3$$$$a=24$$

Commented by mathdanisur last updated on 18/Aug/21

$$\mathrm{Thankyou}\mathrm{Ser}$$

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