A-8-3-21-1-3-8-3-21-1-3-find-A-

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

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

f i n d A

Answered by MJS last updated on 19/Oct/19

A = p^{1 / 3} + q^{1 / 3}

A^{3} = p + q + 3 {(p q)}^{1 / 3} (p^{1 / 3} + q^{1 / 3})

A^{3} - p - q = 3 {(p q)}^{1 / 3} A

{(A^{3} - p - q)}^{3} = 27 {p q A}^{3}

p = 8 + 3 \sqrt{21}

q = 8 - 3 \sqrt{21}

p + q = 16

p q = - 125

{(A^{3} - 16)}^{3} = - 3375 A^{3}

A^{3} - 16 = - 15 A

A^{3} + 25 A - 16 = 0

A = 1

Commented by aliesam last updated on 19/Oct/19

g o d b l e s s y o u s i r

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