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

Toán Lớp 9: √(x-2√x-1)=2 giúp vs !!!!!!!!!!!!!!!!!!!!!!!!!!

Toán Lớp 9: √(x-2√x-1)=2
giúp vs !!!!!!!!!!!!!!!!!!!!!!!!!!

Comments ( 2 )

  1. Giải đáp:
    S={10}.
    Lời giải và giải thích chi tiết:
    \sqrt{x-2\sqrt{x-1}}=2(x>=1)
    <=>\sqrt{x-1-2\sqrt{x-1}+1}=2
    <=>\sqrt{(\sqrt{x-1}-1)^2}=2
    <=>|\sqrt{x-1}-1|=2
    Mà \sqrt{x-1}-1>=-1> -2
    <=>\sqrt{x-1}-1=2
    <=>\sqrt{x-1}=3
    <=>x-1=9
    <=>x=10(tmđk)
    Vậy S={10}.

  2. $\sqrt{x-2\sqrt{x-1}}=2(Đk:x≥1)$
    $x-2\sqrt{x-1}=4$
    $⇔x-1-2\sqrt{x-1}+1=4$
    $⇔(\sqrt{x-1}-1)^2=4(1)$
    Ta có: $\sqrt{x-1}≥0∀x$
    $⇔\sqrt{x-1}-1≥-1>-2$
    $⇒(1)⇔\sqrt{x-1}-1=2$
    $⇔\sqrt{x-1}=3$
    $⇔x-1=9$
    $⇔x=10(t/m)$
    Vậy $x=10$
     

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