Tính
\(4x^2-12x-64y^2+9\)
K
Khách
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H
13 tháng 12 2018
\(2xyz+x^2y+xy^2+x^2z+xz^2+y^2z+yz^2\)
\(=x^2\left(y+z\right)+yz\left(y+z\right)+x\left(y^2+z^3\right)+2xyz\)
\(=\left(y+z\right)\left(x^2+yz\right)+x\left(y^2+z^2+2yz\right)\)
\(=\left(y+z\right)\left(x^2+yz\right)+x\left(y+z\right)^2\)
\(=\left(y+z\right)\left(x^2+yz\right)+xy+xz\)
\(=\left(y+z\right)\left[x\left(x+2\right)+y\left(x+2\right)\right]\)
\(=\left(y+z\right)\left(x+y\right)\left(x+2\right)\)
H
13 tháng 12 2018
\(b,x^2\left(y-z\right)+y^2\left(z-y\right)+z^2\left(x-y\right)\)
\(=x^2\left(y-z\right)+y^2z-y^2x+z^2x-z^2y\)
\(=x^2\left(y-z\right)+yz\left(y-z\right)-x\left(y^2-z^2\right)\)
\(=\left(y-z\right)\left[x^2+yz-x\left(y+z\right)\right]\)
\(=\left(y-z\right)\left[x\left(x-y\right)-z\left(x-y\right)\right]\)
\(=\left(y-z\right)\left[\left(x-z\right)\left(x-y\right)\right]\)
VA
8
13 tháng 12 2018
Ta có: \(\left(1-a\right)\left(1-b\right)=1-a-b+ab\)
-Vì \(a>0;b>0\) nên ab > 0
Suy ra: \(\left(1-a\right)\left(1-b\right)>1-a-b\) (*)
-Vì c < 1 nên 1-c > 0
Tương tự (*) => \(\left(1-a\right)\left(1-b\right)\left(1-c\right)>1-a-b-c\)
\(\Rightarrow\left(1-a\right)\left(1-b\right)\left(1-c\right)\left(1-d\right)>\left(1-a-b-c\right)\left(1-d\right)\)
\(d< 1\Rightarrow d-1>0\)
Vậy \(\left(1-a\right)\left(1-b\right)\left(1-c\right)\left(1-d\right)>1-a-b-c-d\)
=> (đpcm)
14 tháng 12 2018
Đặt \(A=\left(1-a\right)\left(1-b\right)\left(1-c\right)\left(1-d\right)\)
\(A=\left(1-a-b+ab\right)\left(1-c-d+cd\right)\)
\(A=1-c-d+cd-a+ac+ad-acd-b+bd-bcd+ab-abc-abd+abcd+bc\)
\(A=1-a-b-c-d+cd\left(1-a\right)+ac\left(1-b\right)+bc\left(1-d\right)+bd\left(1-c\right)+abcd\)
Có: 0<a,b,c,d<1
=> \(cd\left(1-a\right)>0;ac\left(1-b\right)>0;bc\left(1-d\right)>0;bd\left(1-c\right)>0;abcd>0\)
\(\Rightarrow A>A-cd\left(1-a\right)-ac\left(1-b\right)-bc\left(1-d\right)-bd\left(1-c\right)-abcd=1-a-b-c-d\)
đpcm
ban con choi bangbang ko cho minh muon nick