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

Toán Lớp 7: $(1/3-2x)^{2022}$ + $(3y-x)^{2024}$ = 0

Toán Lớp 7: $(1/3-2x)^{2022}$ + $(3y-x)^{2024}$ = 0

Comments ( 2 )

  1. $\\$
    Giải đáp + giải thích các bước giải :
    (1/3 – 2x)^{2022}+(3y-x)^{2024}=0
    Nhận xét : (1/3 – 2x)^{2022}≥0∀x, (3y-x)^{2024}≥0∀x,y
    Do đó : (1/3 -2x)^{2022}+(3y-x)^{2024}≥0∀∀x,y
    Dấu “=” xảy ra khi :
    (1/3 – 2x)^{2022}=0,(3y-x)^{2024}=0
    ⇔ 1/3 – 2x=0,3y-x=0
    ⇔ x=1/6,3y=x
    ⇔ x=1/6,y=1/18
    Vậy (x;y)=(1/6; 1/18)

  2. Giải đáp:
    x=1/6;y=1/18
    Lời giải và giải thích chi tiết:
    (1/3-2x)^2022+(3y-x)^2024=0
    Ta có:
    {((1/3-2x)^2022ge0forallx),((3y-x)^2024ge0forallx;y):}
    =>(1/3-2x)^2022+(3y-x)^2024ge0forallx;y
    Mà (1/3-2x)^2022+(3y-x)^2024=0
    =>{((1/3-2x)^2022=0),((3y-x)^2024=0):}
    =>{(1/3-2x=0),(3y-x=0):}
    =>{(2x=1/3-0),(3y=0+x):}
    =>{(2x=1/3),(3y=x):}
    =>{(x=1/3:2),(3y=x):}
    =>{(x=1/3 . 1/2),(3y=x):}
    =>{(x=1/6),(3y=1/6):}
    =>{(x=1/6),(y=1/6:3):}
    =>{(x=1/6),(y=1/6 . 1/3):}
    =>{(x=1/6),(y=1/18):}
    Vậy x=1/6;y=1/18

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