Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
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*\(M+\left(5x^2-2xy\right)=6x^2+9xy-y^2\)
\(M=6x^2+9xy-y^2-\left(5x^2-2xy\right)\)
\(M=6x^2+9xy-y^2-5x^2+2xy\)
\(M=\left(6-5\right)x^2+\left(9+2\right)xy-y^2\)
\(M=x^2+11xy-y^2\)
* \(\left(2x-5\right)^{2018}+\left(3y+4\right)^{2020}\le0\)
Ta có : \(\hept{\begin{cases}\left(2x-5\right)^{2018}\ge0\forall x\\\left(3y+4\right)^{2020}\ge0\forall y\end{cases}\Rightarrow}\left(2x-5\right)^{2018}+\left(3y+4\right)^{2020}\ge0\forall x,y\)
Mà đề cho \(\left(2x-5\right)^{2018}+\left(3y+4\right)^{2020}\le0\)
=> \(\left(2x-5\right)^{2018}+\left(3y+4\right)^{2020}=0\)
=> \(\hept{\begin{cases}2x-5=0\\3y+4=0\end{cases}\Rightarrow}\hept{\begin{cases}x=\frac{5}{2}\\y=-\frac{4}{3}\end{cases}}\)
Thay x = 5/2 ; y = -4/3 vào M ta được :
\(M=\left(\frac{5}{2}\right)^2+11\cdot\frac{5}{2}\cdot\left(-\frac{4}{3}\right)-\left(-\frac{4}{3}\right)^2\)
\(M=\frac{25}{4}+\frac{-110}{3}-\frac{16}{9}\)
\(M=\frac{-1159}{36}\)
Vậy giá trị của M = -1159/36 khi x = 5/2 ; y = -4/3
Không chắc nha
a: Xét ΔHAB và ΔHDB có
HA=HD
AB=DB
HB chung
Do đó: ΔHAB=ΔHDB
b: Xét ΔBAI và ΔBDI có
BA=BD
\(\widehat{ABI}=\widehat{DBI}\)
BI chung
Do đó: ΔBAI=ΔBDI
Suy ra: \(\widehat{BAI}=\widehat{BDI}=90^0\)
hay ID⊥BC
\(\dfrac{2^8\cdot9^3}{6^4\cdot4^3}=\dfrac{2^8\cdot3^6}{2^4\cdot3^4\cdot2^6}=\dfrac{2^8\cdot3^6}{2^{10}\cdot3^4}=\dfrac{3^2}{2^2}=\dfrac{9}{4}\)
\(12^5\div\left(2^6\cdot3^8\right)=2^{10}\cdot3^5\div\left(2^6\cdot3^8\right)=\dfrac{2^{10}\cdot3^5}{2^6\cdot3^8}=\dfrac{2^4}{3^3}=\dfrac{16}{27}\)
\(\dfrac{3^{12}\cdot2^{14}\cdot5^5}{10^5\cdot6^8\cdot12^4}=\)\(\dfrac{3^{12}\cdot2^{14}\cdot5^5}{5^5\cdot2^5\cdot2^8\cdot3^8\cdot2^8\cdot3^4}=\)\(\dfrac{3^{12}\cdot2^{14}\cdot5^5}{5^5\cdot2^{21}\cdot3^{12}}=\dfrac{1}{2^7}=\dfrac{1}{128}\)
1) \(\dfrac{2^8\cdot9^3}{6^4\cdot4^3}=\dfrac{2^8\cdot3^6}{2^4\cdot2^6\cdot3^4}=\dfrac{3^2}{2^2}=\dfrac{9}{4}\)
2) \(12^5:\left(2^6\cdot3^8\right)=\dfrac{2^{10}\cdot3^5}{2^6\cdot3^8}=\dfrac{2^4}{3^3}=\dfrac{16}{27}\)
\(\left|x-3\right|=3x-2\Leftrightarrow\hept{\begin{cases}x-3=3x-2\\x-3=-\left(3x-2\right)\end{cases}\Leftrightarrow\hept{\begin{cases}4x=1\\x-3=2-3x\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{1}{4}\\4x=5\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{1}{4}\\x=\frac{5}{4}\end{cases}}}\)
Lời giải:
Gọi tổng trên là $A$
$A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{18.19.20}$
$2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{18.19.20}$
$=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+....+\frac{20-18}{18.19.20}$
$=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{18.19}-\frac{1}{19.20}$
$=\frac{1}{1.2}-\frac{1}{19.20}=\frac{189}{380}$
$\Rightarrow A=\frac{189}{760}$
(1/2-x)^2=(-2)^2
1/2-x=(-2)
x=1/2-(-2)
x=1/2+2
x=1/2+2/1
x=1/2+4/2
x=5/2
26.
\(a.\left(\dfrac{3}{7}\right)^5\cdot x=\left(\dfrac{3}{7}\right)^7\\ =>x=\left(\dfrac{3}{7}\right)^7:\left(\dfrac{3}{7}\right)^5\\ =>x=\left(\dfrac{3}{7}\right)^{7-5}\\ =>x=\left(\dfrac{3}{7}\right)^2\\ =>x=\dfrac{9}{49}\\ b.\left(0,09\right)^3x=-\left(0,09\right)^2\\ =>\left[\left(0,3\right)^2\right]^3\cdot x=-\left[\left(0,3\right)^2\right]^2\\ =>x=-\left(0,3\right)^4:\left(0,3\right)^6\\ =>x=-\left(0,3\right)^{-2}\\ =>x=-\left(\dfrac{10}{3}\right)^2\\ =>x=-\dfrac{100}{9}\)
27:
a: Vì \(0< \dfrac{1}{2}< 1\)
và 40<50
nên \(\left(\dfrac{1}{2}\right)^{40}>\left(\dfrac{1}{2}\right)^{50}\)
b: \(243^3=\left(3^5\right)^3=3^{15};125^5=\left(5^3\right)^5=5^{15}\)
mà 3<5
nên \(243^3< 125^5\)