Toán Lớp 9: Thực hiện phép tính: ∛(26+15 √3) – ∛(26-15 √3)
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Toán Lớp 9: Thực hiện phép tính: ∛(26+15 √3) – ∛(26-15 √3)
Comments ( 1 )
$\sqrt[3]{26+15\sqrt{3}}-\sqrt[3]{26-15\sqrt{3}}$
$=\sqrt[3]{3\sqrt{3}+3.(\sqrt{3})^2.2+3\sqrt{3}.2^2+8}-\sqrt[3]{8-3.4.\sqrt{3}+3.2.3-3\sqrt{3}}$
$=\sqrt[3]{(\sqrt{3}+2)^3}-\sqrt[3]{2-3\sqrt{3})^3}$
$=\sqrt{3}+2-2+\sqrt{3}$
$=2\sqrt{3}$