Question

care este partea intreaga a nr (√2+√5)^2?

Answer 1

   
[tex]\displaystyle\\ ~\left[\left(\sqrt{2}+\sqrt{5}\right)^2\right]=\left[\left(\sqrt{2}\right)^2+2\times \sqrt{2}\times \sqrt{5}+\left(\sqrt{5}\right)^2\right]=\\\\ =\left[\underline{2}+2\sqrt{10}+\underline{5}\right]=\left[7+2\sqrt{10}\right]= 7 +2\times\left[\sqrt{10}\right]\\\\ \boxed{\sqrt{9}\ \textless \ \sqrt{10}\ \textless \ \sqrt{16}~~\Longrightarrow~~ \left[\sqrt{10}\right] = 3}\\\\\\ \Longrightarrow~~7 +2\times\left[\sqrt{10}\right]=7 +2\times 3 =7+6=\boxed{\boxed{\bf 13}}[/tex]

Answer 2

[(√2+√5)²]=[2+5+2√10]=7+[2√10]=7+[√40]
6=√36<√40<√49=7
deci
[√40]=6
atunci numarulcerut este 7+6=13

am preferat asa pt ca la inmultirea unui numar real cu un numar intreg , partea intrega nu este neaparat egala cu produsul intre numarul intreg si partea intreaga a numarului real
deex[2*3,2]=6=2*3dar [2*3,6]=7≠2*3

[9*1.1]=[9,9]=9 dar [9*1,9]=[17,1]=17