19+91=?
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Bỏ dấu ngoặc rồi tính:
a)(2015-79+19)-(-79+19)
b)-(515-80+91)-(2020+80-91)
Giải:
a,Ta có:(2015-79+19)-(-79+19)=2015-79+19+79-19
=2015-79+79+19-19
=2015+0+0=2015
b,-(515-80+91)-(2020+80-91)=-515+80-91-2020-80+91
=-515-2020+80-80-91+91
=-2535+0+0=-2535
a) (2015-79+19)-(-79+19)
= 2015 - 79 +19 + 79 -19
= 2015 + (79- 79) + (19 -19)
= 2015
b) - (515 - 80 +91) -(2020 +80-91)
= -515 + 80 - 91 - 2020 -80 +91
= -515 -2020 +( 80 -80) + (91 -91)
= -2535
\(\dfrac{9}{\sqrt{x-19}}+\dfrac{16}{\sqrt{y-5}}+\dfrac{25}{\sqrt{z-91}}=24-\sqrt{x-19}-\sqrt{y-5}-\sqrt{z-91}\\ \Leftrightarrow\left(\dfrac{9}{\sqrt{x-19}}+\sqrt{x-19}\right)+\left(\dfrac{16}{\sqrt{y-5}}+\sqrt{y-5}\right)+\left(\dfrac{25}{\sqrt{z-91}}+\sqrt{z-91}\right)=24\)
Áp dụng BDT: Cô-si:
\(\Rightarrow\left(\dfrac{9}{\sqrt{x-19}}+\sqrt{x-19}\right)+\left(\dfrac{16}{\sqrt{y-5}}+\sqrt{y-5}\right)+\left(\dfrac{25}{\sqrt{z-91}}+\sqrt{z-91}\right)\ge2\sqrt{\dfrac{9}{\sqrt{x-19}}\cdot\sqrt{x-19}}+2\sqrt{\dfrac{16}{\sqrt{y-5}}\cdot\sqrt{y-5}}+2\sqrt{\dfrac{25}{\sqrt{z-91}}\cdot\sqrt{z-91}}\\ =2\cdot3+2\cdot4+2\cdot5=24\)Dấu "=" xảy ra khi:\(\left\{{}\begin{matrix}\dfrac{9}{\sqrt{x-19}}=\sqrt{x-19}\\\dfrac{16}{\sqrt{y-5}}=\sqrt{y-5}\\\dfrac{25}{\sqrt{z-91}}=\sqrt{z-91}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-19=9\\y-5=16\\z-91=25\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=28\\y=21\\z=116\end{matrix}\right.\)
Vậy các số \(\left\{x;y;z\right\}=\left\{28;21;116\right\}\)
9: \(=\dfrac{47}{51}\cdot\dfrac{17}{94}-\dfrac{47}{51}\cdot\dfrac{53}{91}-\dfrac{53}{91}\cdot\dfrac{91}{53}+\dfrac{53}{91}\cdot\dfrac{47}{51}\)
\(=\dfrac{1}{6}-1=-\dfrac{5}{6}\)
10: \(=\dfrac{13}{19}\cdot\dfrac{19}{26}-\dfrac{13}{19}\cdot\dfrac{71}{43}+\dfrac{71}{43}\cdot\dfrac{13}{19}-\dfrac{71}{43}\cdot\dfrac{86}{71}\)
\(=\dfrac{1}{2}-2=-\dfrac{3}{2}\)
Y + 16 + 10 = 91-19
Y + 16 + 10 = 72
Y + 16 = 72 - 10
Y + 16 = 62
Y = 62 - 16
Y = 46
\(19+\frac{x}{91}=\frac{3}{13}\)
\(=>\frac{x}{91}=\frac{3}{13}-19=\frac{3}{13}-\frac{247}{13}=\frac{-244}{13}\)
\(=>\frac{x}{91}=\frac{-1708}{91}\)
\(=>x=-1708\)
\(19+\frac{x}{91}=\frac{3}{13}\)
<=>\(\frac{x}{91}=\frac{3}{13}-19\)
<=>\(\frac{x}{91}=\frac{-244}{13}\)
<=>\(x=\frac{\left(-244\right).91}{13}\)
,<=>\(x=-1708\)
Tổng của phép tính trên là
19+91=110
Đ/S:110
19+91=110
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