Q. 12 D5.0( 4 Votes )

# If (3x – 1)^{7} = a_{7}x^{7} + a_{6}x^{6} + a_{5}x^{5} + ………..+ a_{1}x + a_{0}, then let us write the value of a_{7} + a_{6} + a_{5} + …….. a_{0} (where a_{7}, a_{6} ……………a_{0} are constants)

Answer :

We have been given that,

(3x – 1)^{7} = a_{7}x^{7} + a_{6}x^{6} + a_{5}x^{5} + … + a_{1}x + a_{0}

If we simply put x = 1 in the above equation,

(3(1) – 1)^{7} = a_{7}(1)^{7} + a_{6}(1)^{6} + a_{5}(1)^{5} + …+ a_{1}(1) + a_{0}

⇒ a_{7} + a_{6} + a_{5} + … + a_{1} + a_{0} = (3 – 1)^{7}

⇒ a_{7} + a_{6} + a_{5} + … + a_{1} + a_{0} = 2^{7}

⇒ a_{7} + a_{6} + a_{5} + … + a_{1} + a_{0} = 128

Thus, value of a_{7} + a_{6} + a_{5} + … + a_{1} + a_{0} = 128.

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