Ai chỉ giúp em bài 2 vs
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\(1,\\ a,\Leftrightarrow\left(x-5\right)\left(x-2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=5\\x=2\end{matrix}\right.\\ b,\Leftrightarrow\left(x-4\right)\left(3x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=4\\x=\dfrac{1}{3}\end{matrix}\right.\\ c,\Leftrightarrow\left(x-7\right)\left(x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=7\\x=-2\end{matrix}\right.\\ d,\Leftrightarrow\left(2x+3\right)\left(2x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\\ 2,\\ a,\Leftrightarrow\left(x+5\right)^2=0\Leftrightarrow x=-5\\ b,\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2=0\Leftrightarrow x=\dfrac{1}{2}\\ c,\Leftrightarrow\left(x-9\right)^2=0\Leftrightarrow x=9\\ d,\Leftrightarrow\left(x-3\right)^3=0\Leftrightarrow x=3\\ e,\Leftrightarrow3x\left(x^2-2x+3\right)=0\\ \Leftrightarrow3x\left(x^2-2x+1+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\\left(x-1\right)^2+2=0\left(vô.nghiệm\right)\end{matrix}\right.\\ \Leftrightarrow x=0\)
\(f,\Leftrightarrow3x\left(x^2-4x+4\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)
Bài 1:
a) \(\Rightarrow\left(x-5\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=5\\x=2\end{matrix}\right.\)
b) \(\Rightarrow3x\left(x-4\right)-\left(x-4\right)=0\)
\(\Rightarrow\left(x-4\right)\left(3x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=4\\x=\dfrac{1}{3}\end{matrix}\right.\)
c) \(\Rightarrow\left(x-7\right)\left(x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=7\\x=-2\end{matrix}\right.\)
d) \(\Rightarrow\left(2x+3\right)\left(2x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)
Bài 2:
a) \(\Rightarrow\left(x+5\right)^2=0\Rightarrow x=-5\)
b) \(\Rightarrow\left(x-\dfrac{1}{2}\right)^2=0\Rightarrow x=\dfrac{1}{2}\)
c) \(\Rightarrow\left(x-9\right)^2=0\Rightarrow x=9\)
d) \(\Rightarrow\left(x-3\right)^3=0\Rightarrow x=3\)
e) \(\Rightarrow3x\left(x^2-6x+9\right)=0\)
\(\Rightarrow3x\left(x-3\right)^2=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
f) \(\Rightarrow3x\left(x^2-4x+4\right)=0\)
\(\Rightarrow3x\left(x-2\right)^2=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)
a/ Tam giác AMN cân tại A (gt). \(\Rightarrow\) \(\widehat{AMN}=\widehat{ANM};AM=AN.\)
Xét tam giác AMB và tam giác ANC có:
+ AM = AN (cmt).
+ \(\widehat{AMB}=\widehat{ANC}\left(\widehat{AMN}=\widehat{ANM}\right).\)
+ MB = NC (gt).
\(\Rightarrow\) Tam giác AMB = Tam giác ANC (c - g - c).
\(\Rightarrow\) AB = AC (cặp cạnh tương ứng).
Xét tam giác ABC có: AB = AC (cmt).
\(\Rightarrow\) Tam giác ABC cân tại A.
b/ Tam giác ABC cân tại A (cmt) \(\Rightarrow\) \(\widehat{ABC}=\widehat{ACB}.\)
Mà \(\widehat{ABC}=\widehat{MBH;}\widehat{ACB}=\widehat{NCK}\text{}\) (đối đỉnh).
\(\Rightarrow\) \(\widehat{MBH}=\widehat{NCK}.\)
Xét tam giác MBH và tam giác NCK \(\left(\widehat{BHM}=\widehat{CKN}=90^o\right)\)có:
+ MB = NC (gt).
+ \(\widehat{MBH}=\widehat{NCK}\left(cmt\right).\)
\(\Rightarrow\) Tam giác MBH = Tam giác NCK (cạnh huyền - góc nhọn).
c/ Tam giác MBH = Tam giác NCK (cmt).
\(\Rightarrow\) \(\widehat{BMH}=\widehat{CNK}\) (cặp góc tương ứng).
Xét tam giác OMN có: \(\widehat{NMO}=\widehat{MNO}\) (do \(\widehat{BMH}=\widehat{CNK}\)).
\(\Rightarrow\) Tam giác OMN tại O.
\(a,=\left(x+y+x-y\right)\left(x+y-x+y\right)=4xy\\ b,=\left(x+y+x-y\right)^2=4x^2\\ c,=\left(x-y+z\right)^2+\left(z-y\right)^2-2\left(x-y+z\right)\left(z-y\right)\\ =\left(x-y+z-z+y\right)^2=x^2\)
\(\left|\frac{2}{3}-\frac{1}{2}+\frac{3}{4}x\right|+\left|1.5-\frac{11}{17}+\frac{23}{13}y\right|=0\)
Mà \(\left|\frac{2}{3}-\frac{1}{2}+\frac{3}{4}x\right|\ge0\) và \(\left|1.5-\frac{11}{17}+\frac{23}{13}y\right|\ge0\)
\(\Rightarrow\left|\frac{2}{3}-\frac{1}{2}+\frac{3}{4}x\right|+\left|1.5-\frac{11}{17}+\frac{23}{13}y\right|\ge0\)
Dấu "="\(\Leftrightarrow\)\(\left|\frac{2}{3}-\frac{1}{2}+\frac{3}{4}x\right|=0\) hoặc \(\left|1.5-\frac{11}{17}+\frac{23}{13}y\right|=0\)
Đến đây dễ r
\(=x^2-1+x-1-x^2-x+x^2-x+2x-2=-x^2\)
\(=-4+x^2+x=-x^2\)
\(=-4+x^2+x+x^2=0\)
\(=-4+2x^2+x=0\Rightarrow x=-1,687\)