October 28th, 2009, 03:34 PM  #1 
Newbie Joined: Oct 2009 Posts: 3 Thanks: 0  The Math Test
Violet was taking a math test. On one problem she was given two positive whole numbers. The problem asked her to square the two numbers and add the squares together. Unforunately, Violet misinterpreted the question. She mistakenly added the two numbers first and squared the result. Her answer was 60 greater than the correct answer to the question. Find all possibilities for the orginal two numbers.

October 28th, 2009, 03:58 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: The Math Test
Let a and b be the two numbers and let x be the value of a² + b². a² + b² = x (a + b)² = x + 60 Expand the lefthand side of (a + b)² = x + 60: a² + 2ab + b² = x + 60 Substitute x = a² + b²: a² + 2ab + b² = a² + b² + 60 2ab = 60, ab = 30, so a and b are factors of 30. 
October 30th, 2009, 06:25 AM  #3 
Newbie Joined: Oct 2009 Posts: 5 Thanks: 0  Re: The Math Test
Can you explain why you explaned the left side?

October 30th, 2009, 06:37 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: The Math Test
To get a² + 2ab + b², which is easier to work with.


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