Prove que os pontos (1, a + b),(a, 1 + b) e (b, 1 + a) são colineares.
Soluções para a tarefa
Respondido por
4
(1, a![\left[\begin{array}{ccc}1&(a + b)&1\\a&(1 + b)&1\\b&(1 + a)&1\end{array}\right] = 0 \\ \\ \\ b(1 + b) + (1 + a) + a(a + b) - [1 + b + b(a + b) + a(1 + a)] = 0 \\ b + b^2 + 1 + a + a^2 + ab - [1 + b + ab + b^2 + a + a^2] = 0 \\ 0 = 0](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B%28a+%2B+b%29%26amp%3B1%5C%5Ca%26amp%3B%281+%2B+b%29%26amp%3B1%5C%5Cb%26amp%3B%281+%2B+a%29%26amp%3B1%5Cend%7Barray%7D%5Cright%5D+%3D+0+%5C%5C+%5C%5C+%5C%5C++b%281+%2B+b%29+%2B+%281+%2B+a%29+%2B+a%28a+%2B+b%29+-+%5B1+%2B+b+%2B+b%28a+%2B+b%29+%2B+a%281+%2B+a%29%5D+%3D+0+%5C%5C+b+%2B+b%5E2+%2B+1+%2B+a+%2B+a%5E2+%2B+ab+-+%5B1+%2B+b+%2B+ab+%2B+b%5E2+%2B+a+%2B+a%5E2%5D+%3D+0+%5C%5C+0+%3D+0 "\left[\begin{array}{ccc}1&(a + b)&1\\a&(1 + b)&1\\b&(1 + a)&1\end{array}\right] = 0 \\ \\ \\ b(1 + b) + (1 + a) + a(a + b) - [1 + b + b(a + b) + a(1 + a)] = 0 \\ b + b^2 + 1 + a + a^2 + ab - [1 + b + ab + b^2 + a + a^2] = 0 \\ 0 = 0")
+ b),(a, 1 + b) e (b, 1 + a)
Perguntas interessantes