Question

please help me be fast. .

Answer 1

Solution:-

let 》
》m is the Arithmetic mean of a and b

》So, m = (a+ b)/2 ⇒2m = a+ b ----(1)

》Again,a , G₁ , G₂ , G₃ and b are in GP .

》So,

》we can assume common ratio r

》G₁ = ar , G₂ = ar² , G₃ = ar³ and b = ar⁴

》b/a = r⁴ -------(2)

》Now,

》G₁⁴ + 2G₂⁴ + G₃⁴ = (ar)⁴ + 2(ar²)⁴ + (ar³)⁴ =

》= a⁴r⁴[1 +2 r⁴ + r⁸ ]

》= a⁴ × b/a × [1 + r⁴]² [ from equation (2) , r⁴= b/a]

》= a³n × [1 + b/a]² = a³n/a²[a + b]² = ba (2m)² 》

》 ( = 4abm²)ans

your answer is option (a) is right