Question

tìm x,y,z biết

a)\(\frac{x}{y}=\frac{7}{3}và5x-2y=87\)

b)\(\frac{x}{19}=\frac{y}{21}và2x-y=34\)

c)\(\left(\frac{-2}{3}\right).x=\left(\frac{-2}{3}\right)^5\)

d)\(\left(\frac{-1}{3}\right)^3.x=\frac{1}{81}\)

Answer 1

*Bài làm:

a, Ta có: \(\frac{x}{y}\) = \(\frac{7}{3}\) (theo đề bài).

⇒ \(\frac{x}{7}\) = \(\frac{y}{3}\)

⇒ \(\frac{5x}{35}\) = \(\frac{2y}{6}\) . Mà \(5x-2y\) = \(87\) .

Áp dụng tính chất dãy tỉ số bằng nhau , ta được:

\(\frac{5x}{35}\) = \(\frac{2y}{6}\) = \(\frac{5x-2y}{35-6}\) = \(\frac{87}{29}\) = \(3\) .

⇒ \(\left\{{}\begin{matrix}\frac{5x}{35}=3\\\frac{2y}{6}=3\end{matrix}\right.\) ⇒ \(\left\{{}\begin{matrix}5x=3.35=105\\2y=3.6=18\end{matrix}\right.\)

⇒ \(\left\{{}\begin{matrix}x=105\div5=21\\y=18\div2=9\end{matrix}\right.\)

➤ Vậy: \(\left(x;y\right)=\left(21;9\right)\) .

b, Ta có: \(\frac{x}{19}\) = \(\frac{y}{21}\)

⇒ \(\frac{2x}{38}\) = \(\frac{y}{21}\) . Mà \(2x-y\) = \(34\) .

Áp dụng tính chất dãy tỉ số bằng nhau , ta được:

\(\frac{2x}{38}\) = \(\frac{y}{21}\) = \(\frac{2x-y}{38-21}\) = \(\frac{34}{17}\) = \(2\) .

⇒ \(\left\{{}\begin{matrix}\frac{2x}{38}=2\\\frac{y}{21}=2\end{matrix}\right.\) ⇒ \(\left\{{}\begin{matrix}2x=2.38=76\\y=2.21=42\end{matrix}\right.\)

⇒ \(\left\{{}\begin{matrix}x=76\div2=38\\y=42\end{matrix}\right.\)

➤ Vậy: \(\left(x;y\right)=\left(38;42\right)\) .

c, Ta có: \(\left(\frac{-2}{3}\right)\) . \(x\) = \(\left(\frac{-2}{3}\right)^5\)

⇒ \(x\) = \(\left(\frac{-2}{3}\right)^5\) \(\div\) \(\left(\frac{-2}{3}\right)\)

⇒ \(x\) = \(\left(\frac{-2}{3}\right)^4\)

⇒ \(x\) = \(\frac{\left(-2\right)^4}{3^4}\)

⇒ \(x\) = \(\frac{16}{81}\)

➤ Vậy: \(x\) = \(\frac{16}{81}\) .

d, Ta có: \(\left(\frac{-1}{3}\right)^3\) . \(x\) = \(\frac{1}{81}\)

⇒ \(\frac{\left(-1\right)^3}{3^3}\) . \(x\) = \(\frac{1}{81}\)

⇒ \(\frac{-1}{27}\) . \(x\) = \(\frac{1}{81}\)

⇒ \(x\) = \(\frac{1}{81}\) \(\div\) \(\frac{-1}{27}\)

⇒ \(x\) = \(\frac{-1}{3}\)

➤ Vậy: \(x\) = \(\frac{-1}{3}\) .

☛ Chúc bạn học tốt!

Answer 2

c) \(\left(-\frac{2}{3}\right).x=\left(-\frac{2}{3}\right)^5\)

=> \(x=\left(-\frac{2}{3}\right)^5:\left(-\frac{2}{3}\right)\)

=> \(x=\left(-\frac{2}{3}\right)^4\)

=> \(x=\frac{16}{81}\)

Vậy \(x=\frac{16}{81}.\)

d) \(\left(-\frac{1}{3}\right)^3.x=\frac{1}{81}\)

=> \(\left(-\frac{1}{27}\right).x=\frac{1}{81}\)

=> \(x=\frac{1}{81}:\left(-\frac{1}{27}\right)\)

=> \(x=-\frac{1}{3}\)

Vậy \(x=-\frac{1}{3}.\)

Chúc bạn học tốt!