\(x^8-y^8=\left(x^4-y^4\right)\left(x^4+y^4\right)=\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\)
\(=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)⋮\left(x-y\right)\)và\(\left(x+y\right)\)(đpcm)
\(x^8-y^8=\left(x^4-y^4\right)\left(x^4+y^4\right)=\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\)
\(=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)⋮\left(x-y\right)\)và\(\left(x+y\right)\)(đpcm)
rút gọn biểu thức
\(\left(x^3+6x^2+12x+8\right)+3\left(x^2+4x+4\right)y+3\left(x+2\right)y^2+y^3\)
1>Tínk:
1, \(\left(x+y\right)^3-\left(x-y\right)^3\)
2, 64-24y+\(3y^2-\dfrac{1}{8}y^3\)
3, \(216x^3+18x^2y+\dfrac{1}{2}xy^2+\dfrac{1}{216}y^3\)
4, \(\left(2x+y\right)^3-3.\left(x+y\right).\left(x-y\right)\)
5, \(\left(x-y\right)^3+3.\left(x+y\right).\left(x^2+y^2\right)\)
Chứng minh :
\(\left(x+y\right)^3-\left(x-y\right)^3=2y\left(3x^2+y^2\right)\)
chứng minh \(\left(y-z\right)^2+\left(z-x\right)^2+\left(x-y\right)^2=\left(y+z-2x\right)^2+\left(z+x-2y\right)^2+\left(y+z-2z\right)^2\)
thì x=y=z
b) \(\left(a+b+c+d\right)\left(a-b+c-d\right)=\left(a^2-b+c-d\right)\left(a+b-c-d\right)\)
thì ad=bc
Chứng minh không tồn tại x,y,z thỏa mãn
a) \(5x^2+10y^2-6xy-4x-2y+3\)=0
b) \(x^2+4y^2+z^2-2x-6x+6y+15=0\)
tìm giá trị nhỏ nhất
a)\(x^2-6x+11\)
b)\(x^2-20x+101\)
c)\(\left(x-1\right)\left(x+2\right)\left(x+3\right)\left(x+6\right)\)
d)\(x^2-2x+y^2+4y+8\)
e)\(x^2-4x+y^2-8y+6\)
f)\(x^2-4xy+5y^2+10x-22y+28\)
giúp mình với mình đang cần
Chứng minh đẳng thức sau:
a) \(\left(x+y\right)^4+x^4+y^4=2.\left(x^2+xy+y^2\right)^2\)
rút gọn
\(\left(2x+y\right)\left(4x^2-2xy+y^2\right)+\left(3x-y\right)\left(9x^2+3xy+y^2\right)-35\left(x-1\right)\left(x^2+x+1\right)\)
\(\left(x+y+z\right)^2-2\left(x+y+z\right)\left(x+y\right)+\left(x+y\right)^2\)
Trg sgk / 17 đó mà tui k hiểu j sất ~.~
chứng minh
\(x^2+y^2\ge2xy\)
\(x^2+y^2\ge\dfrac{\left(x+y\right)^2}{2}\)
\(x^3+y^3\ge xy\left(x+y\right)\)