Question

If a be the AM between b and c GM’s are G₁and G₂, and G₁³ + G₂³ = k abc then value of k is –

• A. 3
• B. 2
• C. 4
• D. 1

Answer 1

Answer: (B)

2

Answer 2

b, a, c are in AP

a = $\frac { b + c } { 2 }$ ̃ 2a = b + c

and b, G₁,G₂, c are in GP

G₁ = br, G₂ = br², c = br³

r = common ratio

̃ G₁³ + G₂³ = (br)³ + (br²)³

= b³r³ + b³r⁶

= b³+ b³

= b²c + bc² = bc (b + c)

= 2 abc

̃ k = 2.