Mă ajută cineva cu câteva exerciții?
Anexe:
![](https://ro-static.z-dn.net/files/d0c/9d506f81f3d2dccde030a3bedaaa7902.jpg)
Răspunsuri la întrebare
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1
1)
![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) 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)](https://tex.z-dn.net/?f=log_%7B2%7D%283%29+%5Ctimes++log_%7B3%7D%284%29+%3D+2+%5C%5C++%5Cfrac%7B+log_%7B3%7D%283%29+%7D%7B+log_%7B3%7D%282%29+%7D++%5Ctimes++log_%7B3%7D%284%29+%3D+2+%5C%5C++%5Cfrac%7B+log_%7B3%7D%284%29+%7D%7B+log_%7B3%7D%282%29+%7D++++%3D+2+%5C%5C++log_%7B2%7D%284%29++%3D+2+%5C%5C+2+%3D+2%28adevarat%29)
2)
![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 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](https://tex.z-dn.net/?f=2x+%2B+y+-+4+%3D+0+%5C%5C+y+%3D+4+-+2x+%5C%5C++%5C%5C++%5C%5C+3x+%2B+y+-+5+%3D+0+%5C%5C+3x+%2B+4+-+2x+-+5+%3D+0+%5C%5C+x+-+1+%3D+0+%5C%5C+x+%3D+1+%5C%5C++%5C%5C++%5C%5C+y+%3D+4+-+2+%5C%5C+y+%3D+2)
4)
![\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 \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](https://tex.z-dn.net/?f=+%5Cfrac%7B%28n+%2B+1%29%21%7D%7B%28n+-+1%29%21%7D+%3D+56+%5C%5C++%5Cfrac%7B%28n+-+1%29%21%28n+%2B+1%29n%7D%7B%28n+-+1%29%21%7D+%3D+56+%5C%5C++%7Bn%7D%5E%7B2%7D++%2B+n+-+56+%3D+0+%5C%5C+delta+%3D+1+%2B+4+%5Ctimes+56+%5C%5C+delta+%3D+225+%5C%5C++%5C%5C+n1+%3D++%5Cfrac%7B+-+1+%2B+15%7D%7B2%7D++%3D++%5Cfrac%7B14%7D%7B2%7D++%3D+7+%5C%5C++%5C%5C+n2+%3D++%5Cfrac%7B+-+1+-+15%7D%7B2%7D++%3D++%5Cfrac%7B+-+16%7D%7B2%7D+%3D++-+8+%5C%5C++%5C%5Csolutie+%5C%3A+finala+%5C%3A++n+%3D+7)
5)
![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 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](https://tex.z-dn.net/?f=c1+%2B+c2+%3D+8+%5C%5C++%5Cfrac%7Bc1++%5Ctimes+c2%7D%7B2%7D++%3D+8+%5C%5C+c1++%5Ctimes++c2+%3D+16+%5C%5C+c1+%3D++%5Cfrac%7B16%7D%7Bc2%7D++%5C%5C++%5C%5C++%5C%5C+c1+%2B+c2+%3D+8+%5C%5C++%5Cfrac%7B16%7D%7Bc2%7D++%2B+c2+%3D+8+%5C%5C++%7Bc2%7D%5E%7B2%7D++-+8c2+%2B+16+%3D+0+%5C%5C++%7B%28c2+-+4%29%7D%5E%7B2%7D++%3D+0+%5C%5C+c2+-+4+%3D+0+%5C%5C+c2+%3D+4+%5C%5C++%5C%5C+c1+%3D+8+-+c2+%5C%5C+c1+%3D+8+-+4+%5C%5C+c1+%3D+4)
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)
2)
4)
5)
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)
Anexe:
![](https://ro-static.z-dn.net/files/d78/59d77374c7cf28a7d482341ebc838922.jpg)
uionutalin:
Poza e pentru exercițiul 4)
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