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Question Number 71756 by aliesam last updated on 19/Oct/19

$$A=\sqrt[3]{8+3\sqrt{21}}+\sqrt[3]{8-3\sqrt{21}}$$$$$$$$findA$$

Answered by MJS last updated on 19/Oct/19

$$A=p^{1/3}+q^{1/3}$$$$A^3=p+q+3{\left(pq\right)}^{1/3}(p^{1/3}+q^{1/3})$$$$A^3-p-q=3{\left(pq\right)}^{1/3}A$$$${(A^3-p-q)}^3=27{pqA}^3$$$$p=8+3\sqrt{21}$$$$q=8-3\sqrt{21}$$$$p+q=16$$$$pq=-125$$$${(A^3-16)}^3=-3375A^3$$$$A^3-16=-15A$$$$A^3+25A-16=0$$$$A=1$$

Commented by aliesam last updated on 19/Oct/19

$$godblessyousir$$

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