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Giải bài tập 3.14 trang 53 SGK Toán 9 tập 1 - Kết nối tri thức

Chứng minh rằng: a) ({left( {1 - sqrt 2 } right)^2} = 3 - 2sqrt 2 ;) b) ({left( {sqrt 3 + sqrt 2 } right)^2} = 5 + 2sqrt 6 .)

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

Toán - Văn - Anh
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Đề bài

Chứng minh rằng: a) \({\left( {1 - \sqrt 2 } \right)^2} = 3 - 2\sqrt 2 ;\) b) \({\left( {\sqrt 3  + \sqrt 2 } \right)^2} = 5 + 2\sqrt 6 .\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Sử dụng hằng đẳng thức đáng nhớ:

💦\({\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2};{\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}\)

Lời giải chi tiết

a) \({\left( {1 - \sqrt 2 } \right)^2}\)\( = {1^2} - 2.1.\sqrt 2  + {\left( {\sqrt 2 } \right)^2}\)\( = 1 - 2\sqrt 2  + 2\)\( = 3 - 2\sqrt 2 ;\) b) \({\left( {\sqrt 3  + \sqrt 2 } \right)^2}\)\( = {\sqrt 3 ^2} + 2.\sqrt 3 .\sqrt 2  + {\left( {\sqrt 2 } \right)^2}\)\( = 3 + 2\sqrt 6  + 2\)\( = 5 + 2\sqrt 6 \)

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