Question

The product of all real values of $t$ satisfying the equation $2^{3t}-4$.$2^{2t}-4$.$2^t+16=0$ is

Answer 1

Given,

$2^{3t}-{4.2}^{2t}-{4.2}^t+16=0$

$\Rightarrow (2^t{)}^3-4.(2^t{)}^2-{4.2}^t+16=0$

let $2^t=x$

$x^3-4x^2-4x+16=0$

$\Rightarrow (x+2)(x-2)(x-4)=0$

$\therefore x=-2$ (Impossible)

$\therefore x=2,x=4$

$\Rightarrow 2^t=2,2^t=4$

$\therefore t=1,t=2$

product $=1\times 2=2$