Exercise 17 Page 482

For any two positive numbers a and b, the geometric mean is the positive number x such that the following equation holds true. a/x=x/bWe are asked to find the geometric mean of the given pair of numbers. 9 and 16 Let's substitute them into the equation and use the Cross Product Property to find the mean x.

9/x=x/16

CrossMult

Cross multiply

x * x = 9 * 16

▼

Solve for x

ProdToPowTwoFac

a* a=a^2

x^2 = 9 * 16

Multiply

Multiply

x^2 = 144

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(x^2)=sqrt(144)

SqrtToAbs

sqrt(a^2)=|a|

|x|=±sqrt(144)

CalcRoot

Calculate root

|x|=± 12

x ≥ 0

x= 12