Question

resolva a equação x√x√x√x...=144​

Answer 1

$\large\boxed{\begin{array}{l}\rm z=x\sqrt{x\sqrt{x\sqrt{x}}}...\\\rm z^2=x^2\underbrace{\rm(x\sqrt{x\sqrt{x\sqrt{x}}}...)}_{z}\\\rm z^2=x^2\cdot z\\\rm como\,z\ne0\\\rm\dfrac{z^2}{z}=\dfrac{x^2\cdot\backslash\!\!\!z}{\backslash\!\!\!z}\\\sf z=x^2\\\rm mas\,x\sqrt{x\sqrt{x\sqrt{x}}}...=144\\\rm ent\tilde ao\\\rm z=144\\\sf x^2=144\\\sf x=\sqrt{144}\\\sf x=12\\\rm Portanto\,a\,soluc_{\!\!,}\tilde ao\,da\,equac_{\!\!,}\tilde ao\\\rm x\sqrt{x\sqrt{x\sqrt{x}}}...=144\\\rm\acute e\,x=12.\end{array}}$