\(P\left(x\right)=-2x^3+3x^2+4x+6\)

\(Q\left(x\right)=-2x^3+2x^2+4x+15\)

\(P\left(x\right)+Q\left(x\right)=-4x^3+5x^2+8x+21\)

\(P\left(x\right)=Q\left(x\right)\)

\(\Leftrightarrow-2x^3+3x^2+4x+6=-2x^3+2x^2+4x+15\)

\(\Leftrightarrow x^2=9\)

\(\Leftrightarrow x=\pm3\)

PT \(\Leftrightarrow\dfrac{x^2+x+1-3x^2-2x^2+2x}{\left(x-1\right)\left(x^2+x+1\right)}=0\left(x\ne1\right)\)

 \(\Leftrightarrow-4x^2+3x+1=0\)

\(\Leftrightarrow-4x^2+4x-x+1=0\)

\(\Leftrightarrow-4x\left(x-1\right)-\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\left(ktm\right)\\x=-\dfrac{1}{4}\left(TMx\ne1\right)\end{matrix}\right.\)

\(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=0\) (\(x,y,z\ne0;x\ne y\ne z\)

\(\Leftrightarrow xy+yz+xz=0\)

\(\Leftrightarrow2yz=yz-xy-xz\)

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

CMTT : \(\left\{{}\begin{matrix}y^2+2xz=\left(y-z\right)\left(y-x\right)\\z^2+2xy=\left(z-x\right)\left(z-y\right)\end{matrix}\right.\)

\(A=\dfrac{yz\left(y-z\right)-xz\left(x-z\right)+xy\left(x-y\right)}{\left(x-y\right)\left(x-z\right)\left(y-z\right)}\)

\(A=\dfrac{y^2z-yz^2-x^2z+xz^2+xy\left(x-y\right)}{\left(x-y\right)\left(x-z\right)\left(y-z\right)}\)

\(A=\dfrac{z^2\left(x-y\right)-z\left(x-y\right)\left(x+y\right)+xy\left(x-y\right)}{\left(x-y\right)\left(x-z\right)\left(y-z\right)}\)

\(A=\dfrac{z^2-xz-yz+xy}{\left(x-z\right)\left(y-z\right)}=\dfrac{x\left(y-z\right)-z\left(y-z\right)}{\left(x-z\right)\left(y-1\right)}=1\)

Thề, gõ máy mệt gấp đôi viết tay =))

Chỗ nào ạ?

Không biết câu c sai đề không thế ạ?

1A

2B

3C

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