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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. The Pythagorean Theorem and Its Converse

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Exercise 58 Page 637

For any two positive numbers a and b, the geometric mean is the positive number x such that ax= xb.

15

Practice makes perfect

For any two positive numbers a and b, the geometric mean is the positive number x such that ax= x b. Since we know that x must be positive, the following equation is the definition of a geometric mean. x= sqrt(a b)We are asked to find the geometric mean of the given pair of numbers. 45 and 5 Let's substitute them into the equation and simplify the right-hand side to find the mean x.

x = sqrt(ab)

a= 45, b= 5

x = sqrt(45 * 5)

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Evaluate right-hand side

Multiply

x = sqrt(225)

Calculate root

x = 15

Subchapter links

Exercises p.633-637