a.

\(\frac{x-1}{x-5}=\frac{6}{7}\)

\(\left(x-1\right)\times7=6\times\left(x-5\right)\)

\(7x-7=6x-30\)

\(7x-6x=-30+7\)

\(x=-23\)

b.

\(\frac{x^2}{6}=\frac{24}{25}\)

\(x^2=\frac{24}{25}\times6\)

\(x^2=\frac{144}{25}\)

\(x^2=\left(\pm\frac{12}{5}\right)^2\)

\(x=\pm\frac{12}{5}\)

Vậy \(x=\frac{12}{5}\) hoặc \(x=-\frac{12}{5}\)

CÓ VẤN ĐỀ ._.

b) \(\frac{x^2}{6}=\frac{24}{25}\)

\(\Rightarrow x.25=24.6\)

\(\Rightarrow x.25=144\)

\(\Rightarrow x=\frac{144}{25}\)

\(\Rightarrow x=5,76\)

Vậy x = 5,76

a) \(\frac{x}{6}^2=\frac{24}{25}\)

\(\Rightarrow x^2.25=6.24\)

\(\Rightarrow x^2.25=144\)

\(\Rightarrow x^2=144\div25\)

\(\Rightarrow x^2=5,76=2,4^2=\left(-2,4^2\right)\)

\(\Rightarrow x\in\left\{2,4;-2,4\right\}\)

Vậy \(x\in\left\{2,4;-2,4\right\}\)

b) \(\frac{72-x}{7}=\frac{x-40}{9}\)

\(\Rightarrow\left(72-x\right).9=\left(x-40\right).7\)

\(\Rightarrow648-9x=7x-280\)

\(\Rightarrow\left(-280\right)-648\) \(=-9x-7x\)

\(\Rightarrow-928=-16x\)

\(\Rightarrow x=58\)

Vậy \(x=58\)

Đặt \(a=24-x,b=x-25\)

Khi đó pt ban đầu trở thành :

\(\frac{a^2+ab+b^2}{a^2-ab+b^2}=\frac{19}{49}\)

\(\Leftrightarrow49\left(a^2+ab+b^2\right)=19\left(a^2-ab+b^2\right)\)

\(\Leftrightarrow30a^2+68ab+30b^2=0\)

\(\Leftrightarrow15a^2+34ab+15b^2=0\)

\(\Leftrightarrow\left(3a+5b\right)\left(5a+3b\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}3a=-5b\\5a=-3b\end{cases}}\)

Đến đây bạn thay vào là dễ rồi nhé ! Chúc bạn học tốt !

a) \(\frac{11}{10,5}=\frac{6,32}{-x}\)

\(6,32:\frac{11}{10,5}=x\)

\(\frac{1659}{275}=x\)

b) \(\frac{x-1}{x+5}=\frac{6}{7}\)

\(\Rightarrow7x-7=6x+30\)

\(7x-6x=30+7\)

\(x=37\)

c) \(\frac{x^2}{6}=\frac{24}{25}\)

\(x^2=\frac{144}{25}\)

\(x=\frac{12}{5}\)

d) \(x:0,16=9:x\)

\(\frac{x}{0,16}=\frac{9}{x}\)

\(x^2=1,44\)

\(x=1,2\)

Áp dụng tính chất của tỉ lệ thức

a) \(\frac{x-1}{x+5}=\frac{6}{7}\)

7( x - 1 ) = 6( x + 5 )

7x - 7 = 6x - 30

7x - 6x = -30 + 7

x = -23

b) \(\frac{x^2}{6}=\frac{24}{25}\)

\(x^2.25=6.24\)

\(x^2.25=144\)

\(x^2=\frac{144}{25}\)

\(x=\sqrt{\frac{144}{25}}\)

\(x=\frac{12}{5}\)

c) \(\frac{x-2}{x-4}=\frac{x+4}{x+7}\)

\(\left(x-2\right)\left(x+7\right)=\left(x+4\right)\left(x-4\right)\)

\(x^2+7x-2x-14=x^2-4x+4x-16\)

\(x^2+5x-14=x^2^{ }-16\)

\(x^2-x^2+5x=-16+14\)

\(5x=-2\)\(x=\frac{-2}{5}\)

a) \(\frac{16}{2^x}=1\Leftrightarrow2^x=16\Leftrightarrow2^x=2^4\Leftrightarrow x=4\)

b)\(5^{x+2}=625\Leftrightarrow5^{x+2}=5^4\Leftrightarrow x+2=4\Leftrightarrow x=2\)

c)\(\frac{x+3}{8}=\frac{2}{x-3}\left(đk:x\ne3\right)\Leftrightarrow\left(x+3\right).\left(x-3\right)=2.8\Leftrightarrow x^2-9=16\Leftrightarrow x^2=25\Leftrightarrow\orbr{\begin{cases}x=5\\x=-5\end{cases}}\)

d)\(\frac{x^2}{6}=\frac{24}{25}\Leftrightarrow25x^2=24.6\Leftrightarrow\left(5x\right)^2=144\Leftrightarrow\orbr{\begin{cases}5x=12\\5x=-12\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{12}{5}\\x=-\frac{12}{5}\end{cases}}\)

a) 16=2^x \(\Leftrightarrow\)x=4

b)5^x+2=5^4\(\Leftrightarrow\)x+2=4\(\Leftrightarrow\)x=2

k đi, mk làm tiếp cho