Question

PLEASE HELP AND EXPLAIN

Let a, b and c be positive numbers such that ab=2, bc=4 and ac=8. What is the value of abc?

Answer 1

It's 8.

Explanation:

ab = 2, bc = 4 and ac = 8.

a^2bc = ab * ac = 2*8 = 16

ab^2 c = 2 * 4 = 8

abc^2 = 32

From the second equation:

b^2 = 8/ac = 8/8 = 1. so b = 1.

Therefore abc = ac*1 = ac = 8

Answer 2

abc = 8

Explanation:

ab=2, bc=4 and ac=8

Multiply all of these together

ac = 2

Multiply by bc =4 (the left on the left and the right on the right)

ac * bc = 2*4

ab^2c =8

Multipy by ac =8 (the left on the left and the right on the right)

ab^2c *ac = 8*8

a^2 b^2 c^2 = 64

Take the square root of each side

sqrt(a^2 b^2 c^2) = ±sqrt(64)

abc = ±8

Since a,b,c are positive numbers

abc = 8