If (3x − y/5) = 10 and xy = 5, Find 27x³ − y³/125
If \[ 3x-\frac{y}{5}=10 \] and \[ xy=5, \] then the value of \[ 27x^3-\frac{y^3}{125} \] is ____________
Solution
\[ \left(3x-\frac{y}{5}\right)^3 = (3x)^3-\left(\frac{y}{5}\right)^3 -3(3x)\left(\frac{y}{5}\right)\left(3x-\frac{y}{5}\right) \]
\[ 10^3 = 27x^3-\frac{y^3}{125} -3\left(\frac{3xy}{5}\right)(10) \]
\[ 1000 = 27x^3-\frac{y^3}{125} -18xy \]
\[ 1000 = 27x^3-\frac{y^3}{125} -18(5) \]
\[ 1000 = 27x^3-\frac{y^3}{125} -90 \]
\[ 27x^3-\frac{y^3}{125} = 1090 \]
\[ \boxed{1090} \]