Question

20%29%29%20%2B%20%20%7B2%7D%5E%7B2%7D%20%20%3D%200" id="TexFormula1" title=" {2}^{x} - 3( {2}(^{x} + \frac{1}{2} )) + {2}^{2} = 0" alt=" {2}^{x} - 3( {2}(^{x} + \frac{1}{2} )) + {2}^{2} = 0" align="absmiddle" class="latex-formula">
Can someone solve this equation?​

Answer 1

Answer:   $\huge\boxed{x=log_2\frac{12\sqrt{2}+4}{17}}$

Step-by-step explanation:                                                                       $\displaystyle\ \bigg{2^x-3(2^{x+\frac{1}{2} }})+2^2=0 \qquad ; \ \ \boxed{t=2^x} \\\\t-3t\sqrt{2} +4=0 \\\\ t(1-3\sqrt{2} )=-4 \\\\ t=\frac{4}{3\sqrt{2} -1} \cdot \frac{3\sqrt{2}+1 }{3\sqrt{2}+1 } =\frac{12\sqrt{2}+4}{17} \\\\\\2^x=\frac{12\sqrt{2}+4}{17} \\\\x=log_2 \ \ \frac{12\sqrt{2}+4}{17}$