Perfect Squares and InspectionDate: 23 May 1995 08:31:25 -0400 From: MUHTAR Newsgroups: local.dr-math Subject:square roots 2+2=?,yapamazsaniz bana sorun !!!! x^1/2+y=11 y^1/2+x=7 what are X?,Y? From: Dr. Ken Newsgroups: local.dr-math Subject: Re: square root problem Date: 23 May 1995 10:41:46 -0400 Hello there! >2+2=?,yapamazsaniz bana sorun !!!! What? I think this is an example of a problem that is best solved the way that most school teachers tell you not to solve math problems: by inspection. The first thing you should notice about the problem is that you've got square roots on the left side, but integers on the right side. Now recall the fact that the only way that the square root of a number can be rational is if the number is a perfect square (that's kind of the definition of a perfect square). So it's possible that x^1/2 is irrational and adding y to it gives you an integer, but it's more likely that the two numbers are perfect squares. Let's go with this strategy first. We know that both numbers are going to be positive, because if one were negative we'd get imaginaries in the left side. So looking at the first equation, what are the perfect squares that are less than 11? These will be your values for y. What does each of these values make x? Try all of these values in the second equation, and you should have your solution! -K |
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