Question

x+2 supra 3 = 27 supra x+2. cu cat este egel x

Answer 1

$\displaystyle \mathtt{ \frac{x+2}{3} = \frac{27}{x+2} \Rightarrow (x+2)(x+2)=3 \cdot 27 \Rightarrow (x+2)^2=81 \Rightarrow } \\ \\ \mathtt{\Rightarrow x^2+2 \cdot x \cdot 2+2^2=81 \Rightarrow x^2+4x+4=81 \Rightarrow x^2+4x+4-81=0\Rightarrow}\\ \\ \mathtt{\Rightarrow x^2+4x-77=0} \\ \\ \mathtt{\Delta=b^2-4ac=4^2-4 \cdot 1 \cdot (-77)=16+308=324\ \textgreater \ 0}$
$\displaystyle \mathtt{x_1= \frac{-b+ \sqrt{\Delta} }{2a} = \frac{-4+ \sqrt{324} }{2 \cdot 1}= \frac{-4+18}{2}= \frac{14}{2}=7}\\ \\ \mathtt{x_2= \frac{-b- \sqrt{\Delta} }{2a}= \frac{-4- \sqrt{324} }{2 \cdot 1}= \frac{-4-18}{2} = \frac{-22}{2} =-11 }$