1)
[tex]log_{2}(3) \times log_{3}(4) = 2 \\ \frac{ log_{3}(3) }{ log_{3}(2) } \times log_{3}(4) = 2 \\ \frac{ log_{3}(4) }{ log_{3}(2) } = 2 \\ log_{2}(4) = 2 \\ 2 = 2(adevarat)[/tex]
2)
[tex]2x + y - 4 = 0 \\ y = 4 - 2x \\ \\ \\ 3x + y - 5 = 0 \\ 3x + 4 - 2x - 5 = 0 \\ x - 1 = 0 \\ x = 1 \\ \\ \\ y = 4 - 2 \\ y = 2[/tex]
4)
[tex] \frac{(n + 1)!}{(n - 1)!} = 56 \\ \frac{(n - 1)!(n + 1)n}{(n - 1)!} = 56 \\ {n}^{2} + n - 56 = 0 \\ delta = 1 + 4 \times 56 \\ delta = 225 \\ \\ n1 = \frac{ - 1 + 15}{2} = \frac{14}{2} = 7 \\ \\ n2 = \frac{ - 1 - 15}{2} = \frac{ - 16}{2} = - 8 \\ \\solutie \: finala \: n = 7[/tex]
5)
[tex]c1 + c2 = 8 \\ \frac{c1 \times c2}{2} = 8 \\ c1 \times c2 = 16 \\ c1 = \frac{16}{c2} \\ \\ \\ c1 + c2 = 8 \\ \frac{16}{c2} + c2 = 8 \\ {c2}^{2} - 8c2 + 16 = 0 \\ {(c2 - 4)}^{2} = 0 \\ c2 - 4 = 0 \\ c2 = 4 \\ \\ c1 = 8 - c2 \\ c1 = 8 - 4 \\ c1 = 4[/tex]
6) AB || CD <=> mAB=mCD
mAB = (yB-yA) / (xB-xA) = 2/2 = 1
mCD = (yC-yD) / (xC-xD) = -2/-2 = 1
De aici => mAB = mCD => AB || CD
4)
