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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Geometric Mean

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Exercise 51 Page 626

Solve the rational equation given by the geometric mean for x.

Example Pairs: 5 and 20 or 9 and 4.
Condition: The product of the numbers must be a perfect square.

Practice makes perfect

By definition, the geometric mean of two positive numbers a and b is the number x such that ax= xb. Let's solve this equation for x.

a/x=x/b ⇒ x=sqrt(ab) Therefore, if we want x to be a whole number, the product of a and b must be a perfect square. Let's see two examples.

a	b	x=sqrt(ab)
5	20	x=sqrt(100)=10
9	4	x=sqrt(36)=6

Subchapter links

Exercises p.623-627