Question

Resolva a equação. (Encontre apenas soluções reais.)

$\mathsf{2x\cdot (4-x)^{-1/2}-3\sqrt{4-x}=0}$

Answer 1

Olá Luan.


Organizando e resolvendo a equação.

Checando a condição de existência para x:

$\mathsf{\sqrt{4-x}\ \textgreater \ 0}\\\\\mathsf{4-x\ \textgreater \ 0}\\\\\mathsf{-x\ \textgreater \ -4~\cdot(-1)}\\\\\mathsf{x\ \textless \ 4}\\\\\mathsf{C.E=\{x\in\mathbb{R}~|~x\ \textless \ 4\}}$

Resolvendo:

$\mathsf{2x\cdot(4-x)^{-1/2}-3\sqrt{4-x}=0}\\\\\mathsf{2x\cdot\dfrac{1}{\sqrt{4-x}}-3\sqrt{4-x}=0~\cdot(\sqrt{4-x})}\\\\\mathsf{2x-3\sqrt{(4-x)^2}=0}\\\\\mathsf{2x-3\cdot(4-x)=0}\\\\\mathsf{2x-12+3x=0}\\\\\mathsf{5x=12}\\\\\mathsf{x=\dfrac{12}{5}}\\\\\boxed{\mathsf{x=2,4}}$

Dúvidas? comente.