Question

Find the value of (2-a)^3+(2-b)^3+(2-c)^3-3(2-a)(2-b)(2-c) when a+b+c=6

Answer 1

$\textbf{Answer:}$

If x+y+z=0

then, x³+y³+z³-3xyz=0

Therefore, If x=2-a, y=2-b, z=2-c

x+y+z=2-a+2-b+2-c=0

=>a+b+c=6

Then, x³+y³+z³-3xyz=0

=(2-a)³+(2-b)³+(2-c)³-3(2a-a)(2a-b)(2a-c)=0

$\textbf{Hope it helps you!}$