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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 9: a)(2+√3)√(7-4√3) b) √(2-√3) .(√6 +√2)

Tháng Tám 14, 2022 Toán học 2 Comments 0 views

Toán Lớp 9: a)(2+√3)√(7-4√3)
b) √(2-√3) .(√6 +√2)

Comments ( 2 )

  1. dongoclandiem
    dongoclandiem
    14 Tháng Tám, 2022 at 3:36 sáng
    Reply
    $\displaystyle \begin{array}{{>{\displaystyle}l}} a) \ \left( 2+\sqrt{3}\right)\sqrt{7-4\sqrt{3}}\\ =\left( 2+\sqrt{3}\right)\sqrt{4-2.2\sqrt{3} +3}\\ =\left( 2+\sqrt{3}\right)\sqrt{\left( 2-\sqrt{3}\right)^{2}}\\ =\left( 2+\sqrt{3}\right) |2-\sqrt{3} |\\ =\left( 2+\sqrt{3}\right)\left( 2-\sqrt{3}\right) \ \left( vì\ 2 >\sqrt{3}\right)\\ =4-3=1\\ b) \ \sqrt{2-\sqrt{3}} .\left(\sqrt{6} +\sqrt{2}\right)\\ =\sqrt{2-\sqrt{3}} .\sqrt{2}\left(\sqrt{3} +1\right)\\ =\sqrt{4-2\sqrt{3}} .\left(\sqrt{3} +1\right)\\ =\sqrt{1-2\sqrt{3} +3} .\left(\sqrt{3} +1\right)\\ =\sqrt{\left( 1-\sqrt{3}\right)^{2}} .\left(\sqrt{3} +1\right)\\ =|1-\sqrt{3} |.\left(\sqrt{3} +1\right)\\ =\left(\sqrt{3} -1\right)\left(\sqrt{3} +1\right) =3-1=2\ \left( vì\ \sqrt{3} >1\right) \ \\ \end{array}$
     

  2. huenthanh97
    huenthanh97
    14 Tháng Tám, 2022 at 3:36 sáng
    Reply
    Giải đáp:
    c) =1
    b)=1
    Lời giải và giải thích chi tiết:
    a) (2+\sqrt{3})\sqrt{7-4\sqrt{3}}
    =(2+\sqrt{3})\sqrt{(\sqrt{4}-4\sqrt{3}+\sqrt{3}}
    =(2+\sqrt{3})\sqrt{(\sqrt{4}-\sqrt{3})^2}
    =(2+\sqrt{3})|\sqrt{4}-\sqrt{3}|
    =(2+\sqrt{3})(\sqrt{4}-\sqrt{3})
    =2\sqrt{4}-2\sqrt{3}+\sqrt{12}-\sqrt{9}
    =4-2\sqrt{3}+2\sqrt{3}-3
    =1
    b) \sqrt{2-\sqrt{3}}(\sqrt{6}+\sqrt{2})
    =\sqrt{(4-2\sqrt{3})/2}(\sqrt{6}+\sqrt{2})
    =\sqrt{((\sqrt{3})^2-2\sqrt{3}+1)/2}(\sqrt{6}+\sqrt{2})
    =\sqrt{((\sqrt{3}-1)^2)/2}(\sqrt{6}+\sqrt{2})
    =|(\sqrt{3}-1)/(\sqrt{2})|(\sqrt{6}+\sqrt{2})
    =(\sqrt{3}-1)/(\sqrt{2}). \sqrt{2}(\sqrt{3}+1)
    =1

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222-9+11+12:2*14+14 = ? ( )

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