Đáp án:
d) \(\left\{ \begin{array}{l}
y = - 5\\
x = - 3
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\left\{ \begin{array}{l}
\dfrac{x}{4} = \dfrac{y}{5}\\
x.y = 20
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{4}{5}y\\
\dfrac{4}{5}y.y = 20
\end{array} \right.\\
\to \left\{ \begin{array}{l}
{y^2} = 25\\
x = \dfrac{4}{5}y
\end{array} \right.\\
\to \left[ \begin{array}{l}
y = 5\\
y = - 5
\end{array} \right. \to \left[ \begin{array}{l}
x = 4\\
x = - 4
\end{array} \right.\\
b)\left\{ \begin{array}{l}
x = \dfrac{3}{2}y\\
{x^3} + {y^3} = - 35
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{{27}}{8}{y^3} + {y^3} = - 35\\
x = \dfrac{3}{2}y
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{{35}}{8}{y^3} = - 35\\
x = \dfrac{3}{2}y
\end{array} \right.\\
\to \left\{ \begin{array}{l}
{y^3} = - 8\\
x = \dfrac{3}{2}y
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = - 2\\
x = - 3
\end{array} \right.\\
c)\left\{ \begin{array}{l}
x = \dfrac{3}{4}y\\
{x^2} + {y^2} = 400
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{9}{{16}}{y^2} + {y^2} = 400\\
x = \dfrac{3}{4}y
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{{25}}{{16}}{y^2} = 400\\
x = \dfrac{3}{4}y
\end{array} \right.\\
\to \left\{ \begin{array}{l}
{y^2} = 256\\
x = \dfrac{3}{4}y
\end{array} \right.\\
\to \left[ \begin{array}{l}
y = 16\\
y = - 16
\end{array} \right. \to \left[ \begin{array}{l}
x = 12\\
x = - 12
\end{array} \right.\\
d)\left\{ \begin{array}{l}
x = \dfrac{3}{5}y\\
{x^3} - {y^3} = 98
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{3}{5}y\\
\dfrac{{27}}{{125}}{y^3} - {y^3} = 98
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{3}{5}y\\
- \dfrac{{98}}{{125}}{y^3} = 98
\end{array} \right.\\
\to \left\{ \begin{array}{l}
{y^3} = - 125\\
x = \dfrac{3}{5}y
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = - 5\\
x = - 3
\end{array} \right.
\end{array}\)
