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14 tháng 10 2021

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 : \(\Rightarrow\hept{\begin{cases}x=3.\left(-\frac{1}{3}\right)=-1\\y=2.\left(-\frac{1}{3}\right)=-\frac{2}{3}\\z=4.\left(-\frac{1}{3}\right)=-\frac{4}{3}\end{cases}}\)

saiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

31 tháng 5 2020

*\(M+\left(5x^2-2xy\right)=6x^2+9xy-y^2\)

\(M=6x^2+9xy-y^2-\left(5x^2-2xy\right)\)

\(M=6x^2+9xy-y^2-5x^2+2xy\)

\(M=\left(6-5\right)x^2+\left(9+2\right)xy-y^2\)

\(M=x^2+11xy-y^2\)

\(\left(2x-5\right)^{2018}+\left(3y+4\right)^{2020}\le0\)

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 

18 tháng 9 2018

\(\left|x-3\right|=3x-2\Leftrightarrow\hept{\begin{cases}x-3=3x-2\\x-3=-\left(3x-2\right)\end{cases}\Leftrightarrow\hept{\begin{cases}4x=1\\x-3=2-3x\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{1}{4}\\4x=5\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{1}{4}\\x=\frac{5}{4}\end{cases}}}\)

19 tháng 10 2017

(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

28 tháng 11 2019

\(\frac{38}{10}:2x=\frac{1}{4}\times\frac{3}{8}\)

\(\frac{38}{10}:2x=\frac{3}{32}\)

\(2x=\frac{38}{10}:\frac{3}{32}\)

\(2x=\frac{38}{10}\times\frac{32}{3}\)

\(2x=\frac{608}{15}\)

\(x=\frac{608}{15}\times\frac{1}{2}\)

\(x=\frac{304}{15}\)

2 tháng 12 2019

\(x-\frac{2}{16}=-\frac{4}{2}-x\)

\(x+x=-\frac{4}{2}+\frac{2}{16}\)

\(2x=-\frac{15}{8}\)

\(x=-\frac{15}{16}\)

2 tháng 12 2019

\(x-\frac{2}{16}=-\frac{4}{2}-x.\)

\(\Leftrightarrow x-\frac{1}{8}=-2-x\)

\(\Leftrightarrow x+x=-2+\frac{1}{8}\)(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^

2 tháng 12 2019


\(\frac{x-2}{16}=\frac{-4}{2-x}\)

\(\Leftrightarrow\frac{x-2}{16}+\frac{4}{2-x}=0\)

\(\Leftrightarrow\frac{\left(x-2\right)\left(2-x\right)+4.16}{16\left(2-x\right)}=0\)

\(\Leftrightarrow\left(x-2\right)\left(2-x\right)+64=0\)

\(\Leftrightarrow-\left(x-2\right)\left(x-2\right)=-64\)

\(\Leftrightarrow-\left(x-2\right)^2=-8^2\)

\(\Leftrightarrow\left(x-2\right)^2=8^2\)

\(\Leftrightarrow\orbr{\begin{cases}x-2=8\\x-2=-8\end{cases}\Leftrightarrow\orbr{\begin{cases}x=10\\x=-6\end{cases}}}\)

2 tháng 12 2019

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