if x+y=7a and xy=12a^2, then find the value of x^3+y^3
You asked:
Given the following equations: \[\begin{aligned}x + y &= 7 a\\ x y &= 12 \cdot {a}^{2}\end{aligned}\] Evaluate \({x}^{3} + {y}^{3}\).
MathBot Answer:
The system of equations has infinitely many solutions.
$$\begin{aligned}a &= \frac{y}{4}\\x &= \frac{3 y}{4}\end{aligned}$$
\(y\) is a free variable.
By substituting these values into the expression, we find that: $$\begin{aligned}x^{3} + y^{3} &= \frac{91 y^{3}}{64}\end{aligned}$$$$\begin{aligned}x^{3} + y^{3} &= \frac{91 y^{3}}{27}\end{aligned}$$