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
\(\left|x-3\right|=3x-2\Leftrightarrow\hept{\begin{cases}x-3=3x-2\\x-3=-\left(3x-2\right)\end{cases}\Leftrightarrow\hept{\begin{cases}4x=1\\x-3=2-3x\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{1}{4}\\4x=5\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{1}{4}\\x=\frac{5}{4}\end{cases}}}\)
(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
\(\frac{38}{10}:2x=\frac{1}{4}\times\frac{3}{8}\)
\(\frac{38}{10}:2x=\frac{3}{32}\)
\(2x=\frac{38}{10}:\frac{3}{32}\)
\(2x=\frac{38}{10}\times\frac{32}{3}\)
\(2x=\frac{608}{15}\)
\(x=\frac{608}{15}\times\frac{1}{2}\)
\(x=\frac{304}{15}\)
\(x-\frac{2}{16}=-\frac{4}{2}-x\)
\(x+x=-\frac{4}{2}+\frac{2}{16}\)
\(2x=-\frac{15}{8}\)
\(x=-\frac{15}{16}\)
\(x-\frac{2}{16}=-\frac{4}{2}-x.\)
\(\Leftrightarrow x-\frac{1}{8}=-2-x\)
\(\Leftrightarrow x+x=-2+\frac{1}{8}\)(xài quy tắc chuyển vế nha)
\(\Leftrightarrow2x=\frac{-16+1}{8}\)
\(\Leftrightarrow2x=-\frac{15}{8}\Rightarrow x=-\frac{15}{8}\div2=-\frac{15}{8}\cdot\frac{1}{2}=-\frac{15}{16}\)
Mình làm hơi quá chi tiết và dài, bạn có thể lược bớt nha.
Học tốt ^3^
\(\frac{x-2}{16}=\frac{-4}{2-x}\)
\(\Leftrightarrow\frac{x-2}{16}+\frac{4}{2-x}=0\)
\(\Leftrightarrow\frac{\left(x-2\right)\left(2-x\right)+4.16}{16\left(2-x\right)}=0\)
\(\Leftrightarrow\left(x-2\right)\left(2-x\right)+64=0\)
\(\Leftrightarrow-\left(x-2\right)\left(x-2\right)=-64\)
\(\Leftrightarrow-\left(x-2\right)^2=-8^2\)
\(\Leftrightarrow\left(x-2\right)^2=8^2\)
\(\Leftrightarrow\orbr{\begin{cases}x-2=8\\x-2=-8\end{cases}\Leftrightarrow\orbr{\begin{cases}x=10\\x=-6\end{cases}}}\)
P/s: Mik nghĩ bài này lớp 8 thì đúng hơn vì nó liên quan đến hằng đẳng thức
Nếu là lp 8 thì giải theo cách này nha:
\(\Rightarrow\left(x-2\right).\left(2-x\right)=16.\left(-4\right)\)
\(2x-x^2-4+2x=-64\)
\(-x^2+4x-4=-64\)
\(-\left(x+2\right)^2=-64\)
\(\Rightarrow\left(x+2\right)^2=8^2\)
\(\Rightarrow\orbr{\begin{cases}x+2=8\\x+2=-8\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=6\\x=-10\end{cases}}\)
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
/x+5/+/x-1/=12:/y+5/+3
suy ra x+5+x-1=12:/y+5/+3 hoặc x+5+x-1=12:-<y+5>+3
Đặt \(\frac{x}{3}=\frac{y}{2}=\frac{z}{4}=k\)
\(\Rightarrow\hept{\begin{cases}x=3k\\y=2k\\z=4k\end{cases}}\)
Thay vào ta có :
\(\left(3k\right)^2+\left(2.2k\right)^2-\left(4k\right)^2=1\)
\(3^2.k^2+\left(4k\right)^2-4^2.k^2=1\)
\(9.k^2+16.k^2-16.k^2=1\)
\(9.k^2=1\)
\(k^2=\frac{1}{9}\)
\(k^2=\left(\frac{1}{3}\right)^2\)hoặc \(\left(-\frac{1}{3}\right)^2\)
\(k=\pm\frac{1}{3}\)
+ Nếu \(k=\frac{1}{3}\)thì : \(\Rightarrow\hept{\begin{cases}x=3.\frac{1}{3}=1\\y=2.\frac{1}{3}=\frac{2}{3}\\z=4.\frac{1}{3}=\frac{4}{3}\end{cases}}\)
+ Nếu \(k=-\frac{1}{3}\)thì : \(\Rightarrow\hept{\begin{cases}x=3.\left(-\frac{1}{3}\right)=-1\\y=2.\left(-\frac{1}{3}\right)=-\frac{2}{3}\\z=4.\left(-\frac{1}{3}\right)=-\frac{4}{3}\end{cases}}\)