Question

If (3x-1)⁷ =a₇x⁷+a₆x⁶+a₅x⁵+….a₁x+a₀, then a₇+a₆+a₅+….+a₁+a₀=
A. 0
B. 1
C. 128
D. 64

Answer 1

Given: (3x - 1)⁷ = a₇x⁷ + a₆x⁶ + a₅x⁵ +…. a₁x + a₀.  

To find : a₇ + a₆ + a₅ +…. + a₁ + a₀ =

 

Solution :  

We have,  (3x - 1)⁷ = a₇x⁷ + a₆x⁶ + a₅x⁵ +…. a₁x + a₀.  

On Putting x = 1, we get

⇒ (3 × 1 – 1)⁷ = a₇(1)⁷ + a₆(1)⁶ + a₅(1)⁵ +…. a₁(1) + a₀.  

⇒ (3  – 1)⁷ = a₇(1) + a₆(1) + a₅(1) +…. a₁(1) + a₀.  

⇒ (2)⁷ = a₇ + a₆  + a₅ +…. a₁ + a₀.  

⇒ a₇ + a₆ + a₅ +…. + a₁ + a₀ = 128

Hence a₇ + a₆ + a₅ +…. + a₁ + a₀ is 128.

Among the given options option (C) 128 is correct.

HOPE THIS ANSWER WILL HELP YOU…..

 

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Answer 2

Step-by-step explanation:

If (3x-1)⁷ =a₇x⁷+a₆x⁶+a₅x⁵+….a₁x+a₀, then a₇+a₆+a₅+….+a₁+a₀=

A. 0

B. 1

C. 128✅✅

D. 64