Question

If (a + b + c) = 4, (1/a + 1/b + 1/c) = 2, and (a² + b² + c²) = 8, find the value of abc.
1. 1
2. 2
3. 5
4. 7

Answer 1

Correct Answer - Option 2 : 2

Given:

(a + b + c) = 4

(1/a + 1/b + 1/c) = 2

(a2 + b2 + c2) = 8

Formula used:

(a + b + c)² = (a2 + b2 + c2) + 2(ab + bc + ac)

Calculation:

According to the question:

(1/a + 1/b + 1/c) = 2

⇒ [(ab + bc + ac)/abc] = 2

⇒ (ab + bc + ac) = 2abc      ----(1)

Now,

(a + b + c)2 = (a2 + b2 + c2) + 2(ab + bc + ac)

From equation (1),

⇒ 42 = 8 + 2 × 2abc

⇒ 16 – 8 = 4abc

⇒ 8 = 4abc

⇒ abc = 8/4 = 2

∴ The value of abc is 2.