Question

Va rog ajutor aduceti la forma mai simpla expresia ( \sqrt{} 10 - \sqrt{19} )+ \sqrt{} 10+ \sqrt{19} ) ^{2}

Answer 1

[tex]E(x)=( \sqrt{10} - \sqrt{19} + \sqrt{10} + \sqrt{19})^2\\\\ Observatie! ~\sqrt{19} ~ si~ - \sqrt{19} ~se~reduc,astfel~obtinem:\\\\ E(x)=( \sqrt{10} + \sqrt{10} )^2\\ MOD~I:E(x)=( \sqrt{10}+ \sqrt{10} )^2\ \textless \ =\ \textgreater \ E(x)=(2 \sqrt{10} )^2=\ \textgreater \ E(x)=40\\ MOD~II:E(x)=( \sqrt{10}+ \sqrt{10} )^2\ \textless \ =\ \textgreater \ E(x)= \sqrt{10}^2+2 \sqrt{10} \sqrt{10} \\+ \sqrt{10} ^2=\ \textgreater \ E(x)=10+2 \sqrt{100}+10=\ \textgreater \ E(x)=10+2*10+10\\ =\ \textgreater \ E(x)=10+20+10=\ \textgreater \ E(x)=30+10=\ \textgreater \ E(x)=40[/tex]