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Mình nhầm xíu :
Tính giá trị của biểu thức :
P = x2015 + y2015 + z2015
Ta có : x3 + y3 = z(3xy - z2)
=> x3 + y3 = 3xyz - z3
=> x3 + y3 + z3 - 3xyz = 0
=> (x + y)(x2 - xy + y2) + z3 - 3xyz = 0
=> (x + y)3 - 3xy(x + y) + z3 - 3xyz = 0
=> [(x + y)3 + z3] - 3xy(x + y) - 3xyz = 0
=> (x + y + z)[(x + y)2 - (x + y)z + z2] - 3xy(x + y + z) = 0
=> (x + y +z)(x2 + y 2 + 2xy - xz - yz + z2) - 3xy(x + y + z) = 0
=> (x + y + z)(x2 + y2 + z2 - xy - yz - zx) = 0
=> x2 + y2 + z2 - xy - yz - zx = 0 (Vì x + y + z = 3)
=> 2(x2 + y2 + z2 - xy - yz - zx) = 0
=> 2x2 + 2y2 + 2z2 - 2xy - 2yz - 2zx = 0
=> (x2 - 2xy + y2) + (y2 - 2yz + z2) + (x2 - 2zx + z2) = 0
=> (x - y)2 + (y - z)2 + (x - z)2 = 0
=> \(\hept{\begin{cases}x-y=0\\y-z=0\\x-z=0\end{cases}}\Rightarrow x=y=z\)
mà x + y + z = 3
=> x = y = z = 1
Khi đó A = 673(x2019 + y2019 + z2019) + 1
= 673(12019 + 12019 + 12019) + 1
= 673.3 + 1 = 2020
Vậy A = 2020
\(\left(x+y+z\right)^2+\left(x-y\right)^2+\left(x-z\right)^2+3\left(x^2+y^2+z^2\right)\)
\(=x^2+y^2+z^2+2\left(xy+yz+xz\right)+x^2-2xy+y^2+x^2-2xz+z^2+3x^2+3y^2+3z^2\)
A phụ thuộc vào biến mà
b gipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipgipụt
BÀI 1:
\(A+B=x^2y+xy^2\)
\(\Leftrightarrow\)\(A+B=xy\left(x+y\right)\)
Vì \(x+y\)\(⋮\)\(13\)
nên \(xy\left(x+y\right)\)\(⋮\)\(13\)
Vậy \(A+B\)\(⋮\)\(13\) nếu \(x+y\)\(⋮\)\(13\)
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