Let `a,b,c`, are non-zero real numbers such that `(1)/(a),(1)/(b),(1)/(c )` are in arithmetic progression and `a,b,-2c`, are in geometric progression, then which of the following statements (s) is (are) must be true?

Options

A. `a^(2),b^(2), 4c^(2)` are in geometric progression
B. `-2a,b, -2c` are in arithmetic progression
C. `a^(3)+b^(3)+c^(3) - 3abc = 0`
D. `a^(2),b^(2),c^(2)` are in harmonic progression

Answer

A, B, C

Explanation

Here, `b=(2ac)/(a+c)" " ……(1)`
and `b^(2)= -2ac" " ….(2)`
`implies b=(-b^(2))/(a+c) implies a+b+c=0`
Now, verify it`