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Giải bài tập 5 trang 54 SGK Toán 9 tập 1 - Cánh diều

Chứng minh: a. (left( {2 - sqrt[{}]{3}} right)left( {2 + sqrt[{}]{3}} right) = 1) b. (left( {sqrt[3]{2} + 1} right)left[ {{{left( {sqrt[3]{2}} right)}^2} - sqrt[3]{2} + 1} right] = 3)

Tổng hợp Đề thi vào 10 có đáp án và lời giải

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Đề bài

Chứng minh: a. \(\left( {2 - \sqrt[{}]{3}} \right)\left( {2 + \sqrt[{}]{3}} \right) = 1\) b. \(\left( {\sqrt[3]{2} + 1} \right)\left[ {{{\left( {\sqrt[3]{2}} \right)}^2} - \sqrt[3]{2} + 1} \right] = 3\)

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Lời giải chi tiết

a. Ta có: \(\left( {2 - \sqrt[{}]{3}} \right)\left( {2 + \sqrt[{}]{3}} \right) = {2^2} - {\left( {\sqrt[{}]{3}} \right)^2} = 4 - 3 = 1\). b. Ta có: \(\left( {\sqrt[3]{2} + 1} \right)\left[ {{{\left( {\sqrt[3]{2}} \right)}^2} - \sqrt[3]{2} + 1} \right] = {\left( {\sqrt[3]{2}} \right)^3} + {1^3} = 2 + 1 = 3\).

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