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If x and y are numbers such that (x+9)(y-9)=0, what is the [#permalink]

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15 Sep 2013, 12:35

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If x and y are numbers such that (x+9)(y-9)=0, what is the smallest possible value of x^2 + y^2

A. 0 B. 9 C. 18 D. 81 E. 162

I understand its a basic question, but I fail to understand the concept. I simply put x+9=0, so x=-9. in the same way, y-9=0, so y=9 so x^2 + y^2 = 81+81=162 what am I doing wrong?

Re: If x and y are numbers such that (x+9)(y-9)=0, what is the [#permalink]

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15 Sep 2013, 12:41

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sandra123 wrote:

If x and y are numbers such that (x+9)(y-9)=0, what is the smallest possible value of x^2 + y^2

A. 0 B. 9 C. 18 D. 81 E. 162

I understand its a basic question, but I fail to understand the concept. I simply put x+9=0, so x=-9. in the same way, y-9=0, so y=9 so x^2 + y^2 = 81+81=162 what am I doing wrong?

From (x+9)(y-9)=0 it follows that either x=-9 or y=9. Thus either x^2=81 or y^2=81.

Now, if x^2=81, then the least value of y^2 is 0, so the least value of x^2 + y^2 = 81 + 0 = 81. Similarly if y^2=81, then the least value of x^2 is 0, so the least value of x^2 + y^2 = 0 + 81 = 81.

Re: If x and y are numbers such that (x+9)(y-9)=0, what is the [#permalink]

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22 Sep 2013, 05:26

sandra123 wrote:

If x and y are numbers such that (x+9)(y-9)=0, what is the smallest possible value of x^2 + y^2

A. 0 B. 9 C. 18 D. 81 E. 162

I understand its a basic question, but I fail to understand the concept. I simply put x+9=0, so x=-9. in the same way, y-9=0, so y=9 so x^2 + y^2 = 81+81=162 what am I doing wrong?

Re: If x and y are numbers such that (x+9)(y-9)=0, what is the [#permalink]

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02 Nov 2014, 23:38

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Re: If x and y are numbers such that (x+9)(y-9)=0, what is the [#permalink]

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