Question

4. Rezolvați ecuația 3[4|2x + 1| - 9] - 16 = 17.​

Answer 1

Răspuns:

3{4 |2x+1|-9}=17+16=33  | :3 ;4 |2x+1 |-9=11 ;  4|2x+1|=11+9=20   | :4 ;|2x+1|=5            2x+1=5 ; 2x=5-1 ;2x=4 ;  x=2 ;  2x+1=-5 ;  2x=-6 ;  x=-3 ;

Explicație pas cu pas:

Answer 2

$\sqrt{(2-\sqrt 5)^2}+x\sqrt{9-4\sqrt 5} = x\sqrt{(2+\sqrt 5)^2}-\sqrt{9+4\sqrt 5}\\ \\ |2-\sqrt 5| +x\sqrt{(2-\sqrt 5)^2} = x|2+\sqrt 5| - \sqrt{(2+\sqrt 5)^2} \\ \\ -(2-\sqrt 5) + x|2-\sqrt 5| = x(2+\sqrt 5) - |2+\sqrt 5| \\ \\ \sqrt 5 - 2 + x(\sqrt 5-2) = x(2+\sqrt 5) - (2+\sqrt 5)\\ \\ x(\sqrt 5-2)-x(2+\sqrt 5) = 2-\sqrt 5 - (2+\sqrt 5)\\ \\ x(\sqrt 5 - 2 - 2 +\sqrt 5) = -2\sqrt 5 \\ \\ -4x = -2\sqrt 5\\ \\ \Rightarrow \boxed{x = \dfrac{\sqrt 5}{2}}$