Question

Urgent!!!dau coroana!!!Solutia reală a ecuatiei (2x - 11)² = 7 este egală cu ....​ !!!!

Answer 1

Răspuns:

$x = \frac{ \sqrt{7 + 11} }{2}$

Explicație pas cu pas:

(2x-11)²=7

$\sqrt{(2x - 11) {}^{2} = 7 }$

$2x - 11 = \sqrt{7}$

$2x = \sqrt{7 } + 11$

$x = \frac{ \sqrt{7 + 11} }{2}$

Answer 2

$\it (2x-11)^2=7 \Rightarrow \sqrt{(2x-11)^2}=\sqrt7 \Rightarrow |2x-11|=\sqrt7 \Rightarrow \\ \\ \Rightarrow -\sqrt7<2x-11<\sqrty7 \Rightarrow 2x-11\in\{-\sqrt7,\ \ \sqrt7\}|_{+11} \Rightarrow \\ \\ \Rightarrow 2x\in\{11-\sqrt7,\ \ 11+\sqrt71\}|_{:2} \Rightarrow x\in\Big\{\dfrac{11-\sqrt7}{2},\ \dfrac{11+\sqrt7}{2}\Big\}$