Suppose the real numbers a,b,x, and y satisfy the equations
ax+by=3,
ax^2+by^2=7,
ax^3+by^3=16,
ax^4+by^4=42.
Evaluate ax^5+by^5.
Suppose the real numbers a,b,x, and y satisfy the equations
ax+by=3,
ax^2+by^2=7,
ax^3+by^3=16,
ax^4+by^4=42.
Evaluate ax^5+by^5.
\(\begin{array}{|rcll|} \hline && ax^5 + b y^5 \\ &=& ( \frac{49}{76}-\frac{457}{76 \cdot \sqrt{87}}) \cdot (-7-\sqrt{87})^5 +( \frac{49}{76}+\frac{457}{76 \cdot\sqrt{87}}) \cdot (\sqrt{87}-7)^5 \\ &=& 20 \\ \hline \end{array}\)
Suppose the real numbers a,b,x, and y satisfy the equations
ax+by=3,
ax^2+by^2=7,
ax^3+by^3=16,
ax^4+by^4=42.
Evaluate ax^5+by^5.
\(\begin{array}{|rcll|} \hline && ax^5 + b y^5 \\ &=& ( \frac{49}{76}-\frac{457}{76 \cdot \sqrt{87}}) \cdot (-7-\sqrt{87})^5 +( \frac{49}{76}+\frac{457}{76 \cdot\sqrt{87}}) \cdot (\sqrt{87}-7)^5 \\ &=& 20 \\ \hline \end{array}\)