What is the solution of 9x – 8 = 34x – 12?

Step-by-step explanation:

Let  

V

be the number of vertices of a polyhedron,  

F

the number of faces of that polyhedron, and  

E

be the number of edges. The quantity  

χ

=

V

−

E

+

F

is called the Euler characteristic (of a polyhedron). In the case of convex polyhedra,  

χ

=

2

.

Consider, for example, a tetrahedron (which is the simplest solid). It has 4 faces,  

1

2

(

4

)

(

3

)

=

6

edges, and  

1

3

(

4

)

(

3

)

=

4

vertices. Thus we have  

V

−

E

+

F

=

4

−

6

+

4

=

2

.

Euler's formula holds for all Platonic solids (tetrahedron, cube, octahedron, dodecahedron, and icosahedron). Since a cube and an octahedron are dual polyhedra (each is formed by connecting the centers of the faces of the other), their  

V

and  

F

values are equal to the  

F

an  

V

values of the other. (The same is true for the dodecahedron and icosahedron).

correct answer:

i^31 = -i