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

Toán Lớp 8: Cho `x+y+z` $\ne$ `0` `x=by+cz` `y=ax+cz` `z=ax+by` Tính `M=1/(1+a) + 1/(1+b) + 1/(1+c)` MONG CHUYÊN GIA GIÚP!!!!!!!!!!!!!!!!!!!!!!!!!!

Tháng Bảy 9, 2022 Toán học 1 Comment 0 views

Toán Lớp 8: Cho x+y+z $\ne$ 0
x=by+cz
y=ax+cz
z=ax+by
Tính M=1/(1+a) + 1/(1+b) + 1/(1+c)
MONG CHUYÊN GIA GIÚP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Comments ( 1 )

  1. ngocbichchau
    ngocbichchau
    9 Tháng Bảy, 2022 at 10:37 sáng
    Reply
    Gửi bạn:
    Ta có:
    $x+y+z=by+cz+ax+cz+ax+by$
    $⇒x+y+z=2ax+2by+2cz$
    $⇒x+y+z=2(ax+by+cz)$
    Vì: $x=by+cz$
    $⇒ax+x=ax+by+cz$
    $⇒x(a+1)=ax+by+cz$
    $⇒\dfrac{1}{a+1}=\dfrac{x}{ax+by+cz}$
    Chứng minh tương tự ta có:
    $\dfrac{1}{b+1}=\dfrac{y}{ax+by+cz}$
    $\dfrac{1}{c+1}=\dfrac{z}{ax+by+cz}$
    $⇒$ $M=\dfrac{1}{a+1}+\dfrac{1}{b+1}+\dfrac{1}{c+1}$
    $=\dfrac{x}{ax+by+cz}+\dfrac{y}{ax+by+cz}+\dfrac{z}{ax+by+cz}$
    $=\dfrac{x+y+z}{ax+by+cz}$
    $=\dfrac{2(ax+by+cz)}{ax+by+cz}$
    $=2$
    Vậy $M=2$
     

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

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