[tex]1)~Notez~cu~x~numarul~de~ani~peste~care~varsta~mamei~va~fi~de \\ trei~ori~mai~mare~decat~varsta~fiicei. \\ \\ 42+x=3(10+x) \Leftrightarrow 42+x=30+3x \Leftrightarrow 12=2x \Rightarrow \boxed{x=6}. \\ \\ Peste~6~ani~varsta~mamei~va~fi~de~trei~ori~mai~mare~decat~varsta \\ fiicei.[/tex]
[tex] x^{2} -3x+m=0 \\ x_{1}=1 \Rightarrow 1 ^{2}-3*1+m=0 \Leftrightarrow -2+m=0 \Rightarrow m=2. \\ \\ x^{2} -3x+m=0 \Leftrightarrow x^{2} -3x+2=0 \\ \Delta= b^{2}-4ac=9-8=1 \\ \\ x_{1,2}= \frac{-b\pm \sqrt{\Delta} }{2a}= \frac{3 \pm1}{2}= \left \{ {{1} \atop {2}} \right. . \\ \\ Cea~de-a~doua~solutie~este~x=2.[/tex]
[tex]a=f( \sqrt{3}) = \sqrt{3}+2 \\ b=f(-\sqrt{3} )=- \sqrt{3}+2 \\ \\ m_{g}(a;b)= \sqrt{ab}= \sqrt{( \sqrt{3}+2)(- \sqrt{3}+2) }= \sqrt{4-3}= \sqrt{1}=1. [/tex]
