Question

(2x-1)^2=2rad2+3

Care este valoare lui x?​

Answer 1

$(2x - 1) \times 2 = 2 \sqrt{2 + 3}$

$2x - 1 = { \sqrt{2 + 3} }$

$2x - 1 = \sqrt{5}$

$2x = \sqrt{5 \times + 1}$

$x = \frac{ \sqrt{5 + 1} }{?}$

supra 2

Nu am reușit să-l pun

Answer 2

$\it (2x-1)^2=2\sqrt2+3 \\ \\ \\ 2\sqrt2+3=3+2\sqrt2=2+1+2\sqrt3=(\sqrt2)^2+2\sqrt2+1^2=(\sqrt2+1)^2$

Ecuația devine:

$\it (2x-1)^2=(\sqrt2+1)^2 \Rightarrow \sqrt{(2x-1)^2}=\sqrt{(\sqrt2+1)^2} \Rightarrow\\ \\ \\ \Rightarrow |2x-1|=\sqrt2+1 \Rightarrow 2x-1=\pm(\sqrt2+1)\\ \\ \\ 2x-1=-(\sqrt2+1)\Rightarrow 2x-1=-\sqrt2-1|_{+1}\Rightarrow 2x=-\sqrt2\Rightarrow \\ \\ \\ \Rightarrow x=\dfrac{-\sqrt2}{2} \Rightarrow x=-\dfrac{\sqrt2}{2}$

$\it 2x-1=+(\sqrt2+1) \Rightarrow 2x-1=\sqrt2+1|_{+1}\Rightarrow 2x=\sqrt2+2|_{:2}\Rightarrow x=\dfrac{\sqrt2+2}{2}$