3x²+16y²+12x-8xy+18=0

<=>(x²-8xy+16y²)+2(x²+6x+9)=0

<=>(x-4y)²+2(x+3)²=0

7) 5x=4y ⇒\(\dfrac{x}{4}=\dfrac{y}{5}\)

Nhân cả hai vế với \(\dfrac{x}{4}\), ta có: \(\left(\dfrac{x}{4}\right)^2=\dfrac{x}{4}.\dfrac{y}{5}=\dfrac{xy}{20}=\dfrac{20}{20}=1\)

\(\left(\dfrac{x}{4}\right)^2=1\Rightarrow\left[{}\begin{matrix}\dfrac{x}{4}=1\\\dfrac{x}{4}=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)

⇒ \(\left[{}\begin{matrix}y=5\\y=-5\end{matrix}\right.\)

4) áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x}{0,5}=\dfrac{y}{0,3}=\dfrac{z}{0,2}=\dfrac{z-y+x}{0,2-0,3+0,5}=\dfrac{1}{\dfrac{2}{5}}=\dfrac{5}{2}\)

\(\dfrac{x}{0,5}=\dfrac{5}{2}\Rightarrow x=\dfrac{5}{4}\)

\(\dfrac{y}{0,3}=\dfrac{5}{2}\Rightarrow y=\dfrac{3}{4}\)

\(\dfrac{z}{0,2}=\dfrac{5}{2}\Rightarrow z=\dfrac{1}{2}\)

6) áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x+11}{13}=\dfrac{y+12}{14}=\dfrac{z+13}{15}=\dfrac{x+11+y+12+z+13}{13+14+15}=\dfrac{42}{42}=1\)

\(\dfrac{x+11}{13}=1\Rightarrow x=2\)

\(\dfrac{y+12}{13}=1\Rightarrow y=1\)

\(\dfrac{z+13}{15}=1\Rightarrow z=2\)

7) \(5x=4y\Rightarrow\dfrac{x}{4}=\dfrac{y}{5}=k\)

\(\Rightarrow x=4k,y=5k\)

\(x.y=20\\ \Rightarrow4k.5k=20\\ \Rightarrow20k^2=20\\ \Rightarrow k^2=1\\ \Rightarrow\left[{}\begin{matrix}k=-1\\k=1\end{matrix}\right.\)

\(x=4k\Rightarrow\left[{}\begin{matrix}x=-4\\x=4\end{matrix}\right.\)

\(y=5k\Rightarrow\left[{}\begin{matrix}y=-5\\y=5\end{matrix}\right.\)

Vậy \(\left(x,y\right)=\left\{\left(-4;-5\right);\left(4;5\right)\right\}\)

\(y\times2+y\times4+y\times0,5=46,8\)

\(y\times\left(2+4+0,5\right)=46,8\)

\(y\times6,5=46,8\)

\(y=46,8:6,5\)

\(y=\dfrac{36}{5}\)

Tính diện tích phần in đậm của hình H, biết cạnh của hình vuông bằng 5cm

1) \(5^x+5^{x+2}=650\)

\(\Rightarrow5^x.1+5^x.5^2=650\)

\(\Rightarrow5^x.\left(1+5^2\right)=650\)

\(\Rightarrow5^x.26=650\)

\(\Rightarrow5^x=650:26\)

\(\Rightarrow5^x=25\)

\(\Rightarrow5^x=5^2\)

\(\Rightarrow x=2\)

Vậy \(x=2.\)

Mình chỉ làm câu 1) thôi nhé.

Chúc bạn học tốt!

y x 6 + y x 3 + y = 80

y x 6 + y x 3 + y x 1 = 80

y x (6+3+1)=80

y x 10 =80

y        =80:10

y       =8

a) \(y\times6+y\times3+y=80\)

\(\Leftrightarrow y\times\left(6+3+1\right)=80\)

\(\Leftrightarrow y\times10=80\)

\(\Leftrightarrow y=80\div10\)

\(\Leftrightarrow y=8\)

b) \(y+y\div0,5+y\div0,25+y\div0,125=15\)

\(\Leftrightarrow y+y\times2+y\times4+y\times8=15\)

\(\Leftrightarrow y\times\left(1+2+4+8\right)=15\)

\(\Leftrightarrow y\times15=15\)

\(\Leftrightarrow y=1\)

a) y x 6 + y x 3 + y = 80

y x (6 + 3 + 1) = 80

y x 10 = 80

y = 80/10

y = 10

b) y + y/0,5 + y/0,25 + y/0,125 = 15

y x 1 + y x 2 + y x 4 + y x 8 = 15

y x (1 + 2 + 4 + 8) = 15

y x 15 = 15

y = 1