Question

Chứng minh rằng: (x+y+z)^3 - x^3 - y^3 - z^3 = 3(x+y)(y+z)(z+x)

Áp dụng: cho x+y+z = 1 , x^2 + y^2 + z^2 = . Tính B= x^2005 + y^2005 + z^2005

 

Answer 1

x^3+y^3+z^3+3(x+y)(y+z)(z+x)-x^3-y^3-z^3=3(x+y)(y+z)(z+x)

Answer 2

tích di

Answer 3

tích cho t nha mn 

Answer 4

ho t tích nha

Answer 5

\(\left(x+y+z\right)^3-x^3-y^3-z^3\)

\(=\left[\left(x+y\right)+z\right]^3-x^3-y^3-z^3\)

\(=\left(x+y\right)^3+z^3+3z\left(x+y\right)\left(x+y+z\right)-x^3-y^3-z^3\)

\(=x^3+y^3+3xy\left(x+y\right)+3z\left(x+y\right)\left(x+y+z\right)-x^3-y^3\)

\(=3xy\left(x+y\right)+3z\left(x+y\right)\left(x+y+z\right)\)

\(=3\left(x+y\right)\left(xy+xz+zy+z^2\right)\)

\(=3\left(x+y\right)\left(y+z\right)\left(z+x\right)\)(đpcm)