Question

CMR

(x-y-z)^2 = x^2 + y^2 + z^2 - 2xy + 2yz - 2zx

Answer 1

\(\left(x-y-z\right)^2=\left[\left(x-y\right)-z\right]^2\)

\(=\left(x-y\right)^2-2z\left(x-y\right)+z^2\)

\(=x^2-2xy+y^2-2xz+2yz+z^2\)

\(=x^2+y^2+z^2-2xy+2yz-2xz\)\(\left(đpcm\right)\)

Answer 2

thanks

Answer 3

Áp dụng HĐT (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca đó bạn. 

Ta có: (x - y + z)^2 >= 0 
<=> x^2 + y^2 + z^2 - 2xy + 2xz - 2yz >= 0 
<=> x^2 + y^2 + z^2 >= 2xy - 2xz + 2yz

Answer 4

\((x+y+z)^2\)

\(=\left(x+y\right)^2+2\left(x+y\right)z+z^2\)

\(=x^2+2xy+y^2+2xz+2xy+z^2\)

~ Hok tốt ~

Answer 5

TL:

Ta có:

\(\left(x-y-z\right)^2=\left[\left(x-y\right)-z\right]^2\)  

\(=\left(x-y\right)^2-2z\left(x-y\right)+z^2\) 

\(=x^2-2xy+y^2-2zx+2zy+z^2\) 

=>đpcm

hc tốt