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b: \(\sqrt{8^2+6^2}-\sqrt{16}+\dfrac{1}{2}\sqrt{\dfrac{4}{25}}\)
\(=10-4+\dfrac{1}{2}\cdot\dfrac{2}{5}=6+\dfrac{1}{5}=\dfrac{31}{5}\)
a, -5/11.7/15.(11/-5)(-30)
=(-5/11.11/-5).(7/15.-30)
=1.7.(-30)/15
=1.7.(-2).15/15
=1.7.(-2)
=-14
b,(11/12):(33/36).3/5
=11/12:(11.3/12.3).3/5
=11/12:11/12.3/5
=1.3/5
=3/5
c,(-5/-9).3/11+(-13/18).3/11
=5/9.3/11+ -13/18.3/11
=3/11.(5/9+ -13/18)
=3/11.(10/18+ -13/18)
=3/11.-3/18
= -9/198
= -1/22
Bài 2:
a,-7/15.5/8.15/7.(-16)
=(-7/15.15/7)(5/8. -16)
= -1.-10
= 10
b,(-1/-2).16/5+(-1/-2)(-11/5)
= 1/2.16/5+1/2. (-11/5)
=1/2.(16/5+ -11/5)
=1/2.5/5
=1/2.1
=1/2
học tốt nha bạn. chúc bạn thành công
b: Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\)
\(\Leftrightarrow\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)
Ta có: \(\dfrac{\left(a+c\right)^2}{\left(b+d\right)^2}\)
\(=\dfrac{\left(bk+dk\right)^2}{\left(b+d\right)^2}\)
\(=k^2\)(1)
Ta có: \(\dfrac{a^2-c^2}{b^2-d^2}\)
\(=\dfrac{\left(bk\right)^2-\left(dk\right)^2}{b^2-d^2}\)
\(=k^2\left(2\right)\)
Từ (1) và (2) suy ra \(\dfrac{\left(a+c\right)^2}{\left(b+d\right)^2}=\dfrac{a^2-c^2}{b^2-d^2}\)
Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\)
\(\Leftrightarrow\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)
Ta có: \(\dfrac{4a+3c}{4b+3d}=\dfrac{4bk+3dk}{4b+3d}=k\)
\(\dfrac{4a-3c}{4b-3d}=\dfrac{4bk-3dk}{4b-3d}=k\)
Do đó: \(\dfrac{4a+3c}{4b+3d}=\dfrac{4a-3c}{4b-3d}\)
a) \(\left|x\right|=3\dfrac{1}{2}\)
\(\Rightarrow\left|x\right|=\dfrac{7}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=-\dfrac{7}{2}\end{matrix}\right.\)
b) \(\left|x-1,2\right|=2,8\)
\(\Rightarrow\left[{}\begin{matrix}x-1,2=2,8\\x-1,2=-2,8\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=4\\x=-1,6\end{matrix}\right.\)
\(a,\left|x\right|=3\dfrac{1}{2}\)
\(\Rightarrow x=\left[{}\begin{matrix}3\dfrac{1}{2}\\-3\dfrac{1}{2}\end{matrix}\right.\)
\(b,\left|x-1,2\right|=2,8\\ \Rightarrow\left[{}\begin{matrix}x-1,2=2,8\\x-1,2=-2,8\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2,8+1,2=4\\x=-2,8+1,2=-1,6\end{matrix}\right.\)
Vậy \(x\in\left\{4;-1,6\right\}\)