ảnh where

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Bài 4: 

\(x=130^0\)

`@` `\text {Ans}`

`\downarrow`

`4,`

Vì `\text {MN // BC}`

`=>` $\widehat {B} = \widehat {BMN} = 114^0 (\text {2 góc đối đỉnh})$

Ta có: \(\left\{{}\begin{matrix}\widehat{\text{BMN}}+\widehat{\text{AMN}}=180^0\left(\text{2 góc kề bù}\right)\\\widehat{\text{CNM}}+\widehat{\text{ANM}}=180^0\left(\text{2 góc kề bù}\right)\end{matrix}\right.\)

`=>`\(\left\{{}\begin{matrix}\widehat{\text{AMN}}=180^0-114^0=66^0\\\widehat{\text{ANM}}=180^0-130^0=50^0\end{matrix}\right.\)

Xét `\Delta AMN`:

\(\widehat{\text{A}}+\widehat{\text{M}}+\widehat{\text{N}}=180^0\left(\text{định lý tổng 3 góc trong 1 tgiac}\right)\)

`=>`\(\widehat{\text{A}}+66^0+50^0=180^0\)

`=>`\(\widehat{\text{A}}=180^0-66^0-50^0=64^0\)

Mà \(\widehat{\text{A}}=\widehat{\text{x}}\)

`=>`\(\widehat{\text{x}}=64^0\)

Vậy, số đo của góc `x = 64^0.`

e: \(E=\dfrac{x^2-9-x^2+4-x^2+9}{\left(x+3\right)\left(x-2\right)}\)

\(=\dfrac{x+2}{x+3}\)

a: \(A=\dfrac{4x^2+x^2-2x+1+x^2+2x+1}{\left(x-1\right)\left(x+1\right)}\)

\(=\dfrac{6x^2+2}{\left(x-1\right)\left(x+1\right)}\)

\(A=\dfrac{-4x^2+x^2-2x+1-x^2-2x-1}{\left(1-x\right)\left(1+x\right)}=\dfrac{-4x\left(x+1\right)}{\left(1-x\right)\left(1+x\right)}=\dfrac{4x}{x-1}\\ C=\dfrac{-x^2-4x-4+x^2-4x+4-4x^2}{\left(x-2\right)\left(x+2\right)}=\dfrac{-4x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{4x}{2-x}\\ E=\dfrac{x^2-9-x^2+4x-4-x^2+9}{\left(x-2\right)\left(x+3\right)}=\dfrac{-\left(x-2\right)^2}{\left(x-2\right)\left(x+3\right)}=\dfrac{2-x}{x+3}\)

a. f(\(\dfrac{-1}{2}\)) = \(4.\left(\dfrac{-1}{2}\right)^2+3.\left(\dfrac{-1}{2}\right)-2\) 

               = \(4.\dfrac{1}{4}-\left(\dfrac{-3}{2}\right)-\dfrac{4}{2}\)

               = \(\dfrac{2}{2}+\dfrac{3}{2}-\dfrac{4}{2}\)

               = \(\dfrac{1}{2}\)

a) (-26) + (-32)   b) 57 + 264   c) (-267) + (-473)   d) (-5) +8

=-(26 + 32)         =321             =-(267 + 473)         =8-5

=-58                                        =-740                     =3

e) 1000 + (-327)    f) (-5679) + 5679   g) (-2364) + (-175)

=1000-327             =0                          =- (2364 + 175)

=673                                                    =-2539

h) 136 + (-36)

=136 - 36

=100

Lời giải:

ĐKĐB $\Rightarrow \frac{2}{c}=\frac{a+b}{ab}\Rightarrow c(a+b)=2ab$

Khi đó:

$\frac{a}{b}-\frac{a-c}{c-b}=\frac{a(c-b)-b(a-c)}{b(c-b)}=\frac{ac-ab-ab+bc}{b(c-b)}=\frac{c(a+b)-2ab}{b(c-b)}=\frac{2ab-2ab}{b(c-b)}=0$

$\Rightarrow \frac{a}{b}=\frac{a-c}{c-b}$ (đpcm)