Write the Value of 30³ + 20³ − 50³
Question:
Write the value of \(30^3 + 20^3 – 50^3\).
Solution
Let
\[ a=30,\quad b=20,\quad c=-50 \]
Then,
\[ a+b+c=30+20-50 \]
\[ a+b+c=0 \]
We know that if \(a+b+c=0\), then
\[ a^3+b^3+c^3=3abc \]
Therefore,
\[ 30^3+20^3-50^3 = 3(30)(20)(-50) \]
\[ =-90000 \]
Therefore,
\[ \boxed{-90000} \]