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

Toán Lớp 8: CMR nếu $a^{4}$ + $b^{4}$ + $c^{4}$ + $d^{4}$ = 4abcd thì a = b = c = d Mong mn giúppp ;-;

Tháng Hai 22, 2023 Toán học 0 Comments 0 views

Toán Lớp 8: CMR nếu $a^{4}$ + $b^{4}$ + $c^{4}$ + $d^{4}$ = 4abcd thì a = b = c = d
Mong mn giúppp ;-;

Comments ( 2 )

  1. hoquyly
    hoquyly
    22 Tháng Hai, 2023 at 4:24 sáng
    Reply
    $\\$
    a^4+b^4+c^4+d^4=4abcd
    =>a^4+b^4+c^4+d^4-4abcd=0
    => (a^4 – 2a^2b^2 + b^4)+(c^4-2c^2d^2+d^4) + (2a^2b^2 – 4abcd + 2c^2d^2)=0
    => (a^2-b^2)^2 + (c^2-d^2)^2 + 2 (ab-cd)^2=0
    Nhận xét :
    (a^2-b^2)^2>=0 ∀ a,b
    (c^2-d^2)^2>=0 ∀c,d
    (ab-cd)^2>= 0∀a,b,c,d
    =>(a^2-b^2)^2+(c^2-d^2)^2+2(ab-cd)^2>=0∀a,b,c,d
    Dấu “=” xảy ra khi :
    (a^2-b^2)^2=0,(c^2-d^2)=0,(ab-cd)^2=0
    <=>a^2-b^2=0,c^2-d^2=0,ab-cd=0
    <=>a=b=c=d
     

  2. bichquyenlien
    bichquyenlien
    22 Tháng Hai, 2023 at 4:24 sáng
    Reply
    Bạn xem hình
     

    toan-lop-8-cmr-neu-a-4-b-4-c-4-d-4-4abcd-thi-a-b-c-d-mong-mn-giuppp

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

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