If 1/a + 1/b + 1/c = 1 / (a + b + c); where a + b + c ≠0; abc ≠ 0, then what…
2024
If 1/a + 1/b + 1/c = 1 / (a + b + c); where a + b + c ≠0; abc ≠ 0, then what is the value of ( a + b ) ( b + c ) ( c + a )?
- A.
Equal to 0
- B.
Greater than 0
- C.
Less than 0
- D.
Cannot be determined
Attempted by 34 students.
Show answer & explanation
Correct answer: A
Solution:
Start with the given equation: 1/a + 1/b + 1/c = 1/(a+b+c). Multiply both sides by abc(a+b+c).
This yields (a+b+c)(ab+bc+ca) = abc.
Use the identity (a+b)(b+c)(c+a) = (a+b+c)(ab+bc+ca) - abc.
Substitute (a+b+c)(ab+bc+ca) = abc into the identity to get (a+b)(b+c)(c+a) = abc - abc = 0.
Therefore the value of (a+b)(b+c)(c+a) is 0.