1) (58 4:15 + 56 7:24): 0,8 +2 1:9 *0,225: 8 3:4*3:5 = (874:15+ 1351:24): 2/5 + 19 : 9*9 : 40 : 35 : 4*3 : 5= (41241/360: 2/5 + 19/40) / 21/4 = (41241/144+ 19/40) / 21/4 = 68849/240 : 21/4= 68849/1260= 54 809/1260
2) (7 1/9 - 2 14/15) : (2 2/3 + 1 3/5) - (3/4-1/20) * (5/7 - 5/14) -48 = (64/9 - 44/15): (8/3 + 8/5) - 7/10*5/14 - 48 = 564/135 : 64/15 - 1/4 - 48 = 47/48 - 1/4 -48 = 35/48 - 48 = - 47 13/48
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Применим формулу разности квадратов:
![{a}^{2} - {b}^{2} = (a - b)(a + b) \\](https://tex.z-dn.net/?f=+%7Ba%7D%5E%7B2%7D++-++%7Bb%7D%5E%7B2%7D++%3D+%28a+-+b%29%28a+%2B+b%29+%5C%5C+)
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![( \: 7 {a}^{2} + 4b)( \: 7 {a}^{2} - 4b) = {(7 {a}^{2} )}^{2} - {(4b)}^{2} = \\ = 49 {a}^{4} - 16 {b}^{2} \\ \\](https://tex.z-dn.net/?f=%28+%5C%3A+7+%7Ba%7D%5E%7B2%7D++%2B+4b%29%28+%5C%3A+7+%7Ba%7D%5E%7B2%7D++-+4b%29+%3D++%7B%287+%7Ba%7D%5E%7B2%7D+%29%7D%5E%7B2%7D++-++%7B%284b%29%7D%5E%7B2%7D++%3D+%5C%5C++%3D+49+%7Ba%7D%5E%7B4%7D++-+16+%7Bb%7D%5E%7B2%7D++%5C%5C++%5C%5C+)
Держи файл тут объяснения и решение\
а)
Вектора коллинеарны когда один вектор можно представить как k*(второй вектор), где k любое число.
отсюда:
![\left \{{{2n=6*k} \atop {4=k*(n+1)}} \right. \\\left \{ {{n=3k} \atop {3k^2+k=4}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B%7B%7B2n%3D6%2Ak%7D+%5Catop+%7B4%3Dk%2A%28n%2B1%29%7D%7D+%5Cright.+%5C%5C%5Cleft+%5C%7B+%7B%7Bn%3D3k%7D+%5Catop+%7B3k%5E2%2Bk%3D4%7D%7D+%5Cright.)
решим квадратное уравнение:
![3k^2+k-4=0\\D=1+48=7^2\\k1,k2=\frac{-1(+-)7}{6}=1;(-\frac{4}{3})\\n1,n2=3;-4;](https://tex.z-dn.net/?f=3k%5E2%2Bk-4%3D0%5C%5CD%3D1%2B48%3D7%5E2%5C%5Ck1%2Ck2%3D%5Cfrac%7B-1%28%2B-%297%7D%7B6%7D%3D1%3B%28-%5Cfrac%7B4%7D%7B3%7D%29%5C%5Cn1%2Cn2%3D3%3B-4%3B)
б) Вектора перпендикулярны когда их скалярное произведение=0;
![12n+(n+1)*4=0\\12n+4n+4=0\\16n=4\\n=\frac{1}{4}](https://tex.z-dn.net/?f=12n%2B%28n%2B1%29%2A4%3D0%5C%5C12n%2B4n%2B4%3D0%5C%5C16n%3D4%5C%5Cn%3D%5Cfrac%7B1%7D%7B4%7D)
Ответ а)3;(-4) б)1/4