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The Renaissance architect Andrea Palladio believed that the height of a room with vaulted ceilings should be the harmonic mean of the length and width.

The harmonic mean of two positive numbers a and b is equal to 2/1/a + 1/b. Simplify this expression. What are the excluded values? What do they mean in this problem?

User David Silveiro
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  • Given: The Renaissance architect Andrea Palladio believed that the height of a room with vaulted ceilings should be the harmonic mean of the length and width. The harmonic mean of two positive numbers a and b is equal to 2/1/a + 1/b.
  • To find: simplify this expression and what are the excluded values and what do they mean in this problem.
  • Simplify the expression by adding the expression in the denominator, then for excluded values check where it is not defined.

The given expression can be simplified as :

2ab/b+a , b ≠ a

The excluded values are a≠b . This mean that the length and width cannot be same.

User Marten Sytema
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