Calculate abc.

Question

Let a,b,c (c<0) be such that ab=1, bc=2, ca=3.

Answer 1

abc=?,  ab=1, bc=2, ca=3.

1*2*3=(ab)(bc)(ca)=(abc)²

abc=√6.

Answer 2

c<0 implies a<0 and b<0

ab=1,   bc=2,   ca=3

b=1/a

(1/a)(c)=2

(c/a)=2

c=2a

(2a)(a)=3

2a²=3

a²=3/2

a=-√3/√2

a=-√6/2

if ab=1, then b is the reciprocal of a, b=-2/√6=-2√6/6=-√6/3

(-√6/3)c=2

c=2(-3/√6)=-6/√6=-6√6/6=-√6

 

Answer 3

If c < 0, then a < 0 and b < 0. (to make products positive!)

b = 1/a, c = 3/a

bc = 2 ⇒ (1/a)(3/a) = 2

3 = 2a²

3/2 = a²

-3√2 / 2 = a

 

Can you determine b and c?