Câu 1:
a: \(\frac{x+4}{y+7}=\frac47\)
=>7(x+4)=4(y+7)
=>7x+28=4y+28
=>7x=4y
=>\(\frac{x}{4}=\frac{y}{7}\)
mà x+y=22
nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\frac{x}{4}=\frac{y}{7}=\frac{x+y}{4+7}=\frac{22}{11}=2\)
=>\(\begin{cases}x=2\cdot4=8\\ y=2\cdot7=14\end{cases}\)
b: \(\frac{x}{3}=\frac{y}{4}\)
=>\(\frac{x}{15}=\frac{y}{20}\left(1\right)\)
\(\frac{y}{5}=\frac{z}{6}\)
=>\(\frac{y}{20}=\frac{z}{24}\left(2\right)\)
Từ (1),(2) suy ra \(\frac{x}{15}=\frac{y}{20}=\frac{z}{24}=k\)
=>x=15k; y=20k; z=24k
\(M=\frac{2x+3y+4z}{3x+4y+5z}\)
\(=\frac{2\cdot15k+3\cdot20k+4\cdot24k}{3\cdot15k+4\cdot20k+5\cdot24k}=\frac{30k+60k+96k}{45k+80k+120k}=\frac{186}{245}\)
Câu 3:
a: \(\frac14\cdot\frac26\cdot\frac38\cdot\ldots\cdot\frac{31}{64}=2^{x}\)
=>\(\frac{1}{64}\cdot\frac24\cdot\frac36\cdot\ldots\cdot\frac{31}{62}=2^{x}\)
=>\(\frac{1}{2^6}\cdot\frac12\cdot\frac12\cdot\ldots\cdot\frac12=2^{x}\) (Với 31-2+1=32-2=30 thừa số 1/2)
=>\(\frac{1}{2^{30+6}}=2^{x}\)
=>\(2^{x}=\frac{1}{2^{36}}\)
=>x=-36
b: \(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\cdot\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^{x}\)
=>\(\frac{4^6}{3^6}\cdot\frac{6^6}{2^6}=2^{x}\)
=>\(\left(\frac43\cdot\frac62\right)^6=2^{x}\)
=>\(2^{x}=2^6\)
=>x=6
