Question

Doua unghiuri complementare $\frac{0,a(b)}{0,b(a)}$ . Aflati toate valorile posibile ale masurilor cele doua unghiuri, stiind ca a+b=6

Answer 1

[tex]\displaystyle \frac{x}{y} = \frac{\overline{ab}-a}{\overline{ba}-b} \\ \frac{x}{y} = \frac{9a+b}{9b+a} \\ \frac{x}{y} =\frac{8a+6}{8b+6}\\ \frac{x}{y+x} =\frac{8a+6}{8b+6+8a+6}\\ \frac{x}{90} =\frac{8a+6}{8(b+a)+12}\\ \frac{x}{90} =\frac{8a+6}{60}\\ x= \frac{90}{60} \cdot 2(4a+3)\\ x=3(4a+3)\\ y=90-x=90-3(4a+3)=3(30-4a-3)=3(27-4a)\\[/tex]
Pentru a=1, b=5=>x=21, y=69
Pentru a=2, y=4=>x=33, y=57
Pentru a=4, y=2=>x=57, y=33
Pentru a=5, y=1=>x=69, y=21