What is the root of the equation 8^t - 2^(2t + 1) + 2^t = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The root of the equation `8^t - 2^(2t + 1) + 2^t = 0` has to be determined.

`8^t - 2^(2t + 1) + 2^t = 0`

=> `(2^3)^t - 2*2^(2t) + 2^t = 0`

=> `(2^t)^3 - 2*(2^t)^2 + 2^t = 0`

Let `2^t = x`

=> `x^3 - 2x^2 + x = 0`

=> `x(x^2 - 2x + 1) = 0`

=> `x(x - 1)^2 = 0`

=> x = 0 and x = 1

As `x = 2^t` and `2^t` cannot take on the value 0, this root can be eliminated.

`2^t = 1`

=> t = 0

The solution of the equation is t = 0

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