Question

determinati solutiile ecuatiilor 4x la a2a -2 =0

Answer 1

$\it 4x^2-2=0 \Rightarrow 4x^2=2 \Rightarrow x^2=\dfrac{\ 2^{(2}}{4} \Rightarrow x^2=\dfrac{1}{2} \Rightarrow \sqrt{x^2}=\sqrt{\dfrac{1}{2}} \Rightarrow\\ \\ \\ \Rightarrow |x| =\sqrt{\dfrac{1}{2}} \Rightarrow x = \pm\sqrt{\dfrac{1}{2}}$

Sau:

$\it 4x^2-2=0|_{:2} \Rightarrow 2x^2-1=0 \Rightarrow (\sqrt2)^2x^2-1^2=0 \Rightarrow\\ \\ \\ \Rightarrow (\sqrt2x)^2-1^2=0 \Rightarrow (\sqrt2 x -1)(\sqrt2 x +1) =0 \Rightarrow\\ \\ \\ \Rightarrow \begin{cases}\it \sqrt2x+1=0 \Rightarrow \sqrt2x=-1 \Rightarrow x=-\dfrac{^{\sqrt2)}1}{\sqrt2} \Rightarrow x_1= -\dfrac{\sqrt2}{2}\\ \\ sau\\ \\ \it \sqrt2x-1=0 \Rightarrow \sqrt2x=1 \Rightarrow x=\dfrac{^{\sqrt2)}1}{\sqrt2} \Rightarrow x_2= \dfrac{\sqrt2}{2}\end{cases}$