Question

Decide!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

a + 1/b = 5

b + 1/c = 12

c + 1/a = 13

manipulating the first line by subtracting 1/b on both sides

a = 5 - 1/b

manipulating the 3rd line by subtracting 1/a on both sides.

c = 13 - 1/a

plugging a into this

c = 13 -1/(5 -1b)

c = 13 -5 +1/b

c= 8 + 1/b

plugging c into the 2nd line

b + 1/(8 +1/b) = 12

b + 1/8 + b = 12

2b + 1/8 = 12

devide both sides by two

b + 1/16 = 6

b = 11 + 15/16

plugging the value for b into the first line to get a

a + 1/(11 + 15/16) = 5

a + 1/11 + 16/15 = 5

a + 15/165 + 176/165 = 5

a + 191/165 = 5

a = 5 + 191/165

a = 1016/165

plugging b into the 2nd line to get c

11 + 15/16 + 1/c = 12

1/c = 1/16

multiply by c on both sides

1 = 1/16c

multiply by 16 on both sides

16 = c

Answer 2

Answer:

Take the first two expressions (you can actually take any two expressions): $\frac{a+b-c}{c}=\frac{a-b+c}{b}$.

$\frac{a+b}{c}=\frac{a+c}{b}$

$ab+b^2=ac+c^2$

$a(b-c)+b^2-c^2=0$

$(a+b+c)(b-c)=0$

$\Rightarrow a+b+c=0$ OR $b=c$

The first solution gives us $x=\frac{(-c)(-a)(-b)}{abc}=-1$.

The second solution gives us $a=b=c$, and $x=\frac{8a^3}{a^3}=8$, which is not negative, so this solution doesn't work.

Therefore, $x=-1\Rightarrow\boxed{A}$.

Step-by-step explanation: