Question

rezolvați ecuația x+1 supra 2 =8 supra x+1 ,x egal tăiat -1​

Answer 1

$\frac{x+1}{2}=\frac{8}{x+1} , \ x \neq -1 \\ \\ (x+1)^2=8\cdot 2\\ \\ x^2+2x+1=16\\ \\ x^2+2x-15=0\\ \\ \Delta=2^2-4\cdot (-15)\cdot 1=4+60=64\\ \\ x_{1, \ 2}=\frac{-2\pm \sqrt{64}}{2\cdot 1}=\frac{-2\pm 8}{2}=-1\pm 4\\ \\ x_1= \ -1+4=3\\ \\ x_2=\ -1-4= \ -5\\ \\ S=\{ -5, \ 3 \}$

Answer 2

$\it \dfrac{x+1}{2}=\dfrac{8}{x+1} \Rightarrow (x+1)(x+1)=2\cdot8 \Rightarrow (x+1)^2=16 \Rightarrow\\ \\ \\ \Rightarrow\sqrt{(x+1)^2}=\sqrt{16} \Rightarrow|x+1|=4 \Rightarrow x+1=\pm4 \Rightarrow x+1\in\{-4,\ 4\}|_{-1}\Rightarrow \\ \\ \\ \Rightarrow x\in\{-5,\ 3\}$