x2+y2+z2+3> hoac = 2(x+y+z)
\(x^2+y^2+z^2+3-2\left(x+y+z\right)\ge0\)
\(\Rightarrow x^2+y^2+z^2+3-2x-2y-2z\ge0\)
\(\Rightarrow\left(x^2-2x+1\right)+\left(y^2-2y+1\right)+\left(z^2-2z+1\right)\ge0\)
\(\Rightarrow\left(x-1\right)^2+\left(y-1\right)^2+\left(z-1\right)^2\ge0\)(Đpcm)
Dấu = khi (x-1)2=(y-1)2=(z-1)2=0 =>x=y=z=1
c) C = x(y2 +z2)+y(z2 +x2)+z(x2 +y2)+2xyz.
d) D = x3(y−z)+y3(z−x)+z3(x−y).
e) E = (x+y)(x2 −y2)+(y+z)(y2 −z2)+(z+x)(z2 −x2).
b) x2 +2x−24 = 0.
d) 3x(x+4)−x2 −4x = 0.
f) (x−1)(x−3)(x+5)(x+7)−297 = 0.
(2x−1)2 −(x+3)2 = 0.
c) x3 −x2 +x+3 = 0.
e) (x2 +x+1)(x2 +x)−2 = 0.
a) A = x2(y−2z)+y2(z−x)+2z2(x−y)+xyz.
b) B = x(y3 +z3)+y(z3 +x3)+z(x3 +y3)+xyz(x+y+z). c) C = x(y2 −z2)−y(z2 −x2)+z(x2 −y2).
phân tích a)(x-y)3+(y-z)3+(z-x)3
b)x.(y2-z2)+y.(z2-x2)+z.(x2-y2)
c)xy.(x-y)-xz.(x+z)-yz.(zx-y+z)
d)x.(y+z)2+y.(z-x)2+z.(x+y)2-4xyz
chung minh rang bieu thuc 4x(x+y)(x+y+z)(x+y) y^2x^2 luon luon khong am voi moi gia tri cua x,y va z
Cho x,y,z t/m: x+y+z=2.Tìm xgtnn của x2+y2+z2-3
phan tich da thuc sau thanh nhan tu
xy(x+y) + yz(y+z) + xz(x+z) + 2xyz
tinh gia tri bieu thuc
3(x-3)(x+7) + (x-4)2 + 48 tai x = 0,5
chung minh rang
x2 - 6x + 10 >0 voi moi x
4x - x2 - 5 <0 voi moi x
cho x+y+z khác 0
x2/y+z + y2/z+x + z2/x+y =1
Tính A=x2/y+z + y2/z+x + z2/x+y
cho cac so thuc x,y,z thoa man 0<a<hoac=x,y,z < hoac=b . tim gia tri lon nhat cua bieu thuc
T= I ab-xy I / (x+y)x + I bc-yz I / (y+z)x + Ica-zxI / (z+x)y
ai lam duoc cau nay minh cong nhan la gioi
Tính giá trị biểu thức:
a) A = 3 x 2 - 2 ( x - y ) 2 - 3 y 2 tại x = 4 và y = -4;
b) B = 4(x - 2)(x +1) + ( 2 x - 4 ) 2 + ( x + 1 ) 2 tại x = - 1 2 ;
c*) C = x 2 (y-z) + y 2 (z-x) + z 2 (x-y) tại x = 6, y = 5 và z = 4;
d*) D = x 2017 - 10 x 2016 + 10 x 2015 - . . . - 10 x 2 + l0x -10 với x = 9.
