2^x =x^2 x=2 x=4 x=−0.76666 ??????????????????? solution please


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Question Number 184376 by Ml last updated on 05/Jan/23

$2^{x} = x^{2}$ $x = 2$ $x = 4$ $x = - 0.76666$ $? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?$ $solution please$
	Answered by Frix last updated on 05/Jan/23
	$2^x =x^2 x=−((2t)/(ln 2)) ⇒ (te^t )^2 =(((ln 2)/2))^2 te^t =±((ln 2)/2) t=W (±((ln 2)/2)) = { ((ln (1/4) ∨ln (1/2))),((≈.265705736221)) :} ⇒ x= { ((4∨2)),((≈−.766664695962)) :}$
	$2^{x} = x^{2}$ $x = - \frac{2 t}{\ln 2}$ $\Rightarrow$ ${(t e^{t})}^{2} = {(\frac{\ln 2}{2})}^{2}$ $t e^{t} = \pm \frac{\ln 2}{2}$ $t = W (\pm \frac{\ln 2}{2}) = {\begin{cases} \ln \frac{1}{4} \lor \ln \frac{1}{2} \\ \approx . 265705736221 \end{cases}$ $\Rightarrow$ $x = {\begin{cases} 4 \lor 2 \\ \approx - . 766664695962 \end{cases}$
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