Need help in solving the following quadratic equations to the power of three...
$\displaystyle x^3-y^3=35$
$\displaystyle x-y=5$
Pls explain or show any relevant working. Thanks in advance for your help.
Use substitution. Solve the 2nd equation for x:
$\displaystyle x = y + 5$
Substitute this into the 1st equation for x:
$\displaystyle \begin{aligned}
x^3 - y^3 &= 35 \\
(y + 5)^3 - y^3 &= 35 \\
y^3 + 15y^2 + 75y + 125 - y^3 &= 35 \\
15y^2 + 75y + 125 &= 35 \\
15y^2 + 75y + 90 &= 0
\end{aligned}$
Solve this quadratic (you'll get two answers for y). Plug both into the equation
$\displaystyle x = y + 5$
to find the corresponding x values.