a) \(\dfrac{7}{9}\times\dfrac{13}{25}\times\dfrac{9}{7}=\left(\dfrac{7}{9}\times\dfrac{9}{7}\right)\times\dfrac{13}{25}=1\times\dfrac{13}{25}=\dfrac{13}{25}\)

b) \(\dfrac{5}{9}\times\dfrac{21}{25}+\dfrac{21}{25}\times\dfrac{4}{9}\)

\(=\dfrac{21}{25}\times\left(\dfrac{5}{9}+\dfrac{4}{9}\right)\)

\(=\dfrac{21}{25}\times1=\dfrac{21}{25}\)

c) \(\dfrac{19}{5}\times\dfrac{11}{16}-\dfrac{9}{5}\times\dfrac{11}{16}\)

\(=\dfrac{11}{16}\times\left(\dfrac{19}{5}-\dfrac{9}{5}\right)\)

\(=\dfrac{11}{16}\times2=\dfrac{22}{16}=\dfrac{11}{8}\)

Lời giải:

\(\frac{4}{9}\times \frac{3}{7}\times \frac{7}{4}=\frac{1}{3}\)

\(\frac{6}{5}\times \frac{4}{5}\times \frac{25}{16}=\frac{3}{2}\)

\(\frac{7}{8}\times \frac{16}{9}\times \frac{3}{14}=\frac{1}{3}\)

theo bài ra ta có:

\(\dfrac{x+16}{9}=\dfrac{y-25}{16}=\dfrac{z+9}{25}\)

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

\(\dfrac{x+16}{9}=\dfrac{y-25}{16}=\dfrac{z+9}{25}=\dfrac{x+16+y-25+z+9}{9+16+25}=\dfrac{x+y+z}{50}\\ \Rightarrow\dfrac{x+16}{9}=\dfrac{x+y+z}{50}\left(1\right)\)ta lại có:

\(\dfrac{9-x}{7}+\dfrac{11-x}{9}=2\\ \Rightarrow\dfrac{7+2-x}{7}+\dfrac{9+2-x}{9}=2\\ \Rightarrow\left(1+\dfrac{2-x}{7}\right)+\left(1+\dfrac{2-x}{9}\right)=2\\ \Rightarrow\left(1+1\right)+\left(\dfrac{2-x}{7}+\dfrac{2-x}{9}\right)=2\\ \Rightarrow2+\left(2-x\right)\left(\dfrac{1}{7}+\dfrac{1}{9}\right)=2\\ \Rightarrow\left(2-x\right)\left(\dfrac{1}{7}+\dfrac{1}{9}\right)=0\\ \Rightarrow2-x=0\\ \Rightarrow x=2\)

thay x = 2 vào 1 ta có:

\(\Rightarrow\dfrac{2+16}{9}=\dfrac{x+y+z}{50}\\ \Rightarrow\dfrac{18}{9}=\dfrac{x+y+z}{50}\\ \Rightarrow2=\dfrac{x+y+z}{50}\\ \Rightarrow x+y+z=2.50\\ \Rightarrow x+y+z=100\)

vậy x + y + z = 100

Từ \(\frac{9-x}{7}+\frac{11-x}{9}=2\)

\(=>\frac{9-x}{7}+\frac{11-x}{9}-2=0\)

\(=>\frac{9-x}{7}+\frac{11-x}{9}-1-1=0\)

\(=>\left(\frac{9-x}{7}-1\right)+\left(\frac{11-x}{9}-1\right)=0\)

\(=>\frac{2-x}{7}+\frac{2-x}{9}=0=>\left(2-x\right).\left(\frac{1}{7}+\frac{1}{9}\right)=0\)

Vì \(\frac{1}{7}+\frac{1}{9}\) khác 0=>2-x=0=>x=2

Theo T/c dãy tỉ số=nhau:

\(\frac{x+16}{9}=\frac{y-25}{16}=\frac{z+9}{25}=\frac{x+16+y-25+z+9}{9+16+25}\)\(=\frac{\left(x+y+z\right)+\left(16-25+9\right)}{9+16+25}=\frac{x+y+z}{50}\)

Thay x=2 vào \(\frac{x+16}{9}=>\frac{2+16}{9}=\frac{x+y+z}{50}=>\frac{x+y+z}{50}=2=>x+y+z=100\)

Vậy x+y+z=100

\((x+9)(x^2-25)=0\)
\(\Rightarrow\orbr{\begin{cases}x+9=0\\x^2-25=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-9\\x\in\left\{-5;5\right\}\end{cases}}}\)
\((x-7)(16+x^2)(25-x^2)=0\)
\(\Rightarrow\hept{\begin{cases}x-7=0\\16+x^2=0\\25-x^2=0\end{cases}\Rightarrow\hept{\begin{cases}x=7\left(TM\right)\\x^2=-16\left(KTM\right)\\x\in\left\{-5;5\right\}\end{cases}}}\)
Học tốt!