Question

1) Rút gọn biểu thức

a)A=3x-| 2x+5| -7

b)B=| x+5| -| 2x+7| -4x

2) Tìm x

a)| x+4| +| x-2| =6

b)| 4x+3| -x=5

3) Cho tỉ lệ thúc a/b=c/d. CM rằng ta có các tỉ lệ thức sau

a)\(\left(\dfrac{a+b}{c+d}\right)^2=\dfrac{a^2+b^2}{c^2+d^2}\)

b)\(\dfrac{2a+3b}{2a-3b}=\dfrac{2c+3d}{2c-3d}\)

HELP ME. Mai15/8 18:30 mik đi học rồi. Các bạn giúp mik với mik sẽ tick cho các bạn

Answer 1

\(\dfrac{a}{b}=\dfrac{c}{d}=k\Rightarrow\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)

\(\Rightarrow\left(\dfrac{a+b}{c+d}\right)^2=\left[\dfrac{\left(bk+b\right)}{\left(dk+d\right)}\right]^2=\left[\dfrac{b\left(k+1\right)}{d\left(k+1\right)}\right]^2=\dfrac{b^2}{d^2}\)

\(\Rightarrow\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{b^2k^2+b^2}{d^2k^2+d^2}=\dfrac{b^2\left(k+1\right)}{d^2\left(k+1\right)}=\dfrac{b^2}{d^2}\)

Vậy...

\(\dfrac{2a+3b}{2a-3b}=\dfrac{2bk+3b}{2bk-3b}=\dfrac{b\left(2k+3\right)}{b\left(2k-3\right)}=\dfrac{2k+3}{2k-3}\)

\(\dfrac{2c+3d}{2c-3d}=\dfrac{2dk+3d}{2dk-3d}=\dfrac{d\left(2k+3\right)}{d\left(2k-3\right)}=\dfrac{2k+3}{2k-3}\)

Vậy...