Đáp án:
`2/(xy) - 9 = 1/z^2 => 2/(xy) - 1/z^2 = 9`
`1/x + 1/y + 1/z = 3`
`<=> (1/x + 1/y + 1/z)^2 = 9`
`<=> 1/x^2 + 1/y^2 + 1/z^2 + 2/(xy) + 2/(yz) + 2/(zx) = 2/(xy) - 1/z^2 `
`<=> 1/x^2 + 1/y^2 + 1/z^2 + 2/(xy) + 2/(yz) + 2/(zx) - 2/(xy) + 1/z^2 = 0`
`<=> 1/x^2 + 1/y^2 + 2/(z^2) + 2/(yz) + 2/(zx) = 0`
`<=> (1/x^2 + 2/(xz) + 1/z^2) + (1/z^2 + 2/(zy) + 1/y^2) = 0`
`<=> (1/x + 1/z)^2 + (1/z + 1/y)^2 = 0`
`<=> 1/x + 1/z = 0`
`1/z + 1/y = 0`
`<=> x = y = -z`
Có : `1/x + 1/y + 1/z = 3`
`<=> -1/z + -1/z + 1/z = 3`
`<=> -1/z = 3`
`<=> z = -1/3`
`<=> x = y = 1/3`
Do đó `(x + 3y + z)^{2019} = [1/3 + 3. (1)/3 + (-1)/3]^{2019} = [1/3 + 1 + (-1)/3]^{2019} = 1^{2019} = 1`
Giải thích các bước giải:
