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If √x √y+√z=0, which of the following is true?
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28 Mar 2016, 22:43
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If \(√x √y+√z=\)0, which of the following is true? A. \(x^2+y^2+z^2=xy+xz+yz\) B. \(x^2+y^2+z^2=2xy+2xz+2yz\) C. \(x^2+y^2z^2=2xy+2xz2yz\) D. \(x^2y^2z^2=xy+xz+yz\) E. \(x^4+y^4+z^4=2xy+2xz+2yz\) * A solution will be posted in two days.
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Re: If √x √y+√z=0, which of the following is true?
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29 Mar 2016, 00:51
MathRevolution wrote: If √x √y+√z=0, which of the following is true?
A. x^2+y^2+z^2=xy+xz+yz B. x^2+y^2+z^2=2xy+2xz+2yz C. x^2+y^2z^2=2xy+2xz2yz D. x^2y^2z^2=xy+xz+yz E. x^4+y^4+z^4=2xy+2xz+2yz
\(\sqrt{x} + \sqrt{z} = \sqrt{y}\) \(x + z + 2\sqrt{xz} = y\) \(x + z  y = 2\sqrt{xz}\) \((a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\) \(x^2 + z^2 + y^2 + 2xz  2yz  2xy = 4xz\) \(x^2 + y^2 + z^2 = 2xy + 2yz + 2xz\) Answer: B



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Re: If √x √y+√z=0, which of the following is true?
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30 Mar 2016, 23:21
If √x √y+√z=0, which of the following is true? A. x^2+y^2+z^2=xy+xz+yz B. x^2+y^2+z^2=2xy+2xz+2yz C. x^2+y^2z^2=2xy+2xz2yz D. x^2y^2z^2=xy+xz+yz E. x^4+y^4+z^4=2xy+2xz+2yz If you square the both equations, they become x+z+2√xz=y, x+zy=2√xz. If you once again square the both equations, x^2+z^2+y^2+2zx2xy2zy=4xz is derived and eventually becomes x^2+y^2+z^2=2xy+2yz+2zx. Thus, the answer is B.
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Re: If √x √y+√z=0, which of the following is true?
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25 Dec 2017, 05:49
MathRevolution wrote: If √x √y+√z=0, which of the following is true?
A. x^2+y^2+z^2=xy+xz+yz B. x^2+y^2+z^2=2xy+2xz+2yz C. x^2+y^2z^2=2xy+2xz2yz D. x^2y^2z^2=xy+xz+yz E. x^4+y^4+z^4=2xy+2xz+2yz
* A solution will be posted in two days. In case one does not remembers the formula, plugging smart numbers will be highly effective. Let \(x=z=1\) & \(y=4\). this satisfies our stem equation. Test the values in the options and the option where \(LHS=RHS\) will be correct For Option B \(LHS=1^2+4^2+1^2=18\) \(RHS=2*1*4+2*1*1+2*4*1=18\). For other options, LHS will not be equal to RHS



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Re: If √x √y+√z=0, which of the following is true?
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27 Dec 2017, 09:51
MathRevolution wrote: If √x √y+√z=0, which of the following is true?
A. x^2+y^2+z^2=xy+xz+yz B. x^2+y^2+z^2=2xy+2xz+2yz C. x^2+y^2z^2=2xy+2xz2yz D. x^2y^2z^2=xy+xz+yz E. x^4+y^4+z^4=2xy+2xz+2yz
If you square the both equations, they become x+z+2√xz=y, x+zy=2√xz. If you once again square the both equations, x^2+z^2+y^2+2zx2xy2zy=4xz is derived and eventually becomes x^2+y^2+z^2=2xy+2yz+2zx. Thus, the answer is B. Thank you. Could you help me understand where the highlighted portion came from?



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If √x √y+√z=0, which of the following is true?
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27 Dec 2017, 09:56
rb60006 wrote: MathRevolution wrote: If √x √y+√z=0, which of the following is true?
A. x^2+y^2+z^2=xy+xz+yz B. x^2+y^2+z^2=2xy+2xz+2yz C. x^2+y^2z^2=2xy+2xz2yz D. x^2y^2z^2=xy+xz+yz E. x^4+y^4+z^4=2xy+2xz+2yz
If you square the both equations, they become x+z+2√xz=y, x+zy=2√xz. If you once again square the both equations, x^2+z^2+y^2+2zx2xy2zy=4xz is derived and eventually becomes x^2+y^2+z^2=2xy+2yz+2zx. Thus, the answer is B. Thank you. Could you help me understand where the highlighted portion came from? Hi rb60006we can rearrange the equation and write \(\sqrt{x}+\sqrt{z}=\sqrt{y}\), so on squaring it will be of the form \((a+b)^2=a^2+b^2+2ab\)



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Re: If √x √y+√z=0, which of the following is true?
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09 Jan 2018, 08:31
Is this a 700 level question?



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Re: If √x √y+√z=0, which of the following is true?
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09 Jan 2018, 08:37
kritikalal wrote: Is this a 700 level question? Hi kritikalalCheck the "Tag" section just above the question. you will get all the details



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Re: If √x √y+√z=0, which of the following is true?
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14 May 2019, 00:20
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Re: If √x √y+√z=0, which of the following is true?
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