\(1)\left(x+y+x\right)\left(x+y-z\right)\)
\(=xx+xy+xz+\left(yx+yy+yz\right)+ \left(-zx-zy-zz\right)\)
\(=x^2+xy+xz+yx+y^2+yz-zx-zy-z^2\)
\(=x^2+2xy+y^2+yz+0-zy-z^2\)
\(=x^2+2xy+y^2+yz-zy-z^2\)
\(=x^2+2xy+y^2+0-z^2\)
\(=x^2+2xy+y^2-z^2\)
rút gọn biểu thức :
a,[x+y]^2.[x-y]^2
b,2.[x-y][x+y]+[x+y]^2+[x-y]^2
c,[x-y+z]^2+[z-y]^2+2.[x-y+z][y-z]
tìm x,y,z
a)x+y+z=1;x2+y2+z2=1;\(x^2+y^3+z^3=1\)
Cho x,y,z khác 0 và x+y+z=0 . Tính:
A=\(\dfrac{x^2}{y^2+z^2-x^2}+\dfrac{y^2}{z^2+x^2-y^2}+\dfrac{z^2}{x^2+y^2-z^2}\)
Rút gọn
a) M= (x + y + z)2 + (y + z)2 - 2(y + z) . (x + y +z)
b) N= (x - 1)3 + (x + 1)3
Rút gọn biểu thức:
a,A=(x - y + z)2 + ( z - y )2 + 2(x - y + z)(y - z)
b,B=(5x -1) + 2(1-5x)(4 + 5x) + ( 5x + 4)2
c,C=(x - y )3 + ( y+ x)3 + ( y - x)3 - 3xy( x + y)
(x-y+x)2 + (z-y)2 + 2(x-y+z)(y+z)
Chứng minh rằng nếu:
(x-y)2+(y-z)2+(x-z)2=(x+y-2z)2+(z+x-2y)2+(y+z-2x)2thì x=y=z
Chứng minh rằng nếu:\(\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2=\left(y+z-2x\right)^2+\left(z+x-2y\right)^2+\left(x+y-2z\right)^2\)thì x=y=z
Bài 1: Rút gọn:
a,(x+y)\(^2\)+(x-y)\(^2\)
b, 2(x-y)(x+y)+(x+y)\(^2\)+(x-y)\(^2\)
c,(x-y+z)\(^2\)+(z-y)\(^2\)+2(x-y+z)(y-z)
