Question

Hey...vreau si eu cat mai repede ajutor va rog
Fie c=(2x+3) la puterea 2 -(2x+3)(2x-3). Afla a, b € Q , stiind ca x= radical din 3 si c=a radical din 3 +b
raspunsul e a=12
b=18

Answer 1

   
[tex]\displaystyle\\ c=(2x+3)^2 -(2x+3)(2x-3) =\\\\= (2x+3)[(2x+3)-(2x-3)] =\\\\ =(2x+3)[\underline{2x}+3-\underline{2x}+3] =\\\\ = (2x+3)(3+3)=6(2x+3)=\boxed{\bf12x+18}\\\\ c = 12x+18 ~~\text{si}~~x = \sqrt{3} ~~\Longrightarrow~~c = \boxed{\bf12\sqrt{3}+18}\\\\ c=a\sqrt{3} +b\\\\ 12\sqrt{3}+18 = a\sqrt{3} +b\\\\ \Longrightarrow\Longrightarrow\\\\ 12\sqrt{3}=a\sqrt{3} ~~\Longrightarrow~~a = \frac{12\sqrt{3}}{\sqrt{3}} = \boxed{\bf12}\\\\ 18 = b ~~\Longrightarrow~~ b = \boxed{\bf 18}[/tex]