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a: \(7+\left(\dfrac{7}{12}-\dfrac{1}{2}+3\right)-\left(\dfrac{1}{12}+5\right)\)
\(=7+\dfrac{7}{12}-\dfrac{1}{12}-\dfrac{1}{2}+3-5\)
\(=7+1-2\)
=6
c) \(1-\left\{1:\left[2^3+1-\left(-\dfrac{1}{2}\right)^2\right]\right\}\)\(=1-\left[1:\left(8+1-\dfrac{1}{4}\right)\right]=1-\left(1:\dfrac{35}{4}\right)=1-\dfrac{4}{35}\)\(=\dfrac{35-4}{35}=\dfrac{31}{35}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Ta có: \(\widehat{xBC}=\widehat{ABM}\)
mà \(\widehat{ABM}=\widehat{NMB}\)
nên \(\widehat{xBC}=\widehat{BMN}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : \(B\left(x\right)=2x+3-3x-x^4+4x^3+x^2+2x^4-4x^3+x+5\)
\(=x^4+x^2+8=0\)( vô lí )
Vì \(x^4\ge0\forall x;x^2\ge0\forall x;8>0\)
Vậy đa thức B(x) vô nghiệm
![](https://rs.olm.vn/images/avt/0.png?1311)
d)s=8+7^2+7^3+...+7^99=1+7+7^2+7^3+...+7^99
7s=7+7^2+7^3+7^4+...+7^100
7s-s=7^100-1
s=(7^100-1)/6
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 4:
a) Vì $ABC$ cân tại $A$ nên $AB=AC$ và $\widehat{ABC}=\widehat{ACB}$
$\Rightarrow 180^0-\widehat{ABC}=180^0-\widehat{ACB}$
hay $\widehat{ABQ}=\widehat{ACR}$
Xét tam giác $ABQ$ và $ACR$ có:
$AB=AC$ (cmt)
$\widehat{ABQ}=\widehat{ACR}$ (cmt)
$BQ=CR$ (gt)
$\Rightarrow \triangle ABQ=\triangle ACR$ (c.g.c)
$\Rightarrow AQ=AR$
b)
$H$ là trung điểm của $BC$ nên $HB=HC$
Mà $QB=CR nên $HB+QB=HC+CR$ hay $QH=HR$
Xét tam giác $AQH$ và $ARH$ có:
$AQ=AR$ (cmt)
$QH=RH$ (cmt)
$AH$ chung
$\Rightarrow \triangle AQH=\triangle ARH$ (c.c.c)
$\Rightarrow \widehat{QAH}=\widehat{RAH}$
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{\left(-3\right)^2.3^3.625}{\left(-5\right)^6.\left|-81\right|}=\dfrac{3^2.3^3.5^4}{5^6.81}=\dfrac{3^5.5^4}{5^6.3^4}=\dfrac{3}{5^2}=\dfrac{3}{25}\)
b: \(x^2-\dfrac{16}{25}=0\)
\(\Leftrightarrow x^2=\dfrac{16}{25}\)
hay \(x\in\left\{\dfrac{4}{5};-\dfrac{4}{5}\right\}\)
b) \(x^2-\dfrac{16}{25}=0\Rightarrow x^2=\dfrac{16}{25}\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{4}{5}\\x=-\dfrac{4}{5}\end{matrix}\right.\)
c) \(\dfrac{2}{5}-\left|\dfrac{1}{2}-x\right|=6\)
\(\Rightarrow\left|\dfrac{1}{2}-x\right|=-\dfrac{28}{5}\)(vô lý do \(\left|\dfrac{1}{2}-x\right|\ge0\))
Vậy \(S=\varnothing\)