Question

4^x+2^x=6
Rezolvati ecuatia

Answer 1

${4}^{x} + {2}^{x} = 6$

${ ({2}^{2} )}^{x} + {2}^{x} - 6 = 0$

${ ({2}^{x}) }^{2} + {2}^{x} - 6 = 0$

${2}^{x} = t \: \: \: ,t > 0$

${t}^{2} + t - 6 = 0$

$a = 1$

$b = 1$

$c = - 6$

$\Delta = {b}^{2} - 4ac$

$\Delta = {1}^{2} - 4 \times 1 \times ( - 6)$

$\Delta = 1 + 24$

$\Delta = 25$

$t_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a} = \frac{ - 1 \pm \sqrt{25} }{2 \times 1} = \frac{ - 1 \pm5}{2}$

$t_{1} = \frac{ - 1 + 5}{2} = \frac{4}{2} = 2 = > {2}^{x} = 2 = > x = 1$

$t_{2} = \frac{ - 1 - 5}{2} = - \frac{6}{2} = - 3 \: nu \: convine$