Toán 9 Rút gọn $k=\sqrt[3]{7+5\sqrt{2}}-\sqrt[3]{20+14\sqrt{2}}$

Ann Lee

Ann Lee

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[tex]k=\sqrt[3]{7+5\sqrt{2}}-\sqrt[3]{20+14\sqrt{2}}\\k=\sqrt[3]{2\sqrt{2}+6+3\sqrt{2}+1}-\sqrt[3]{2\sqrt{2}+12+12\sqrt{2}+8}\\k=\sqrt[3]{(\sqrt{2}+1)^3}-\sqrt[3]{(\sqrt{2}+2)^3}\\k=(\sqrt{2}+1)-(\sqrt{2}+3)\\k=-2[/tex]
 
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