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1/x+1/y=1 xy=6, then what is the value of x^2+y^2? [#permalink]
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19 Jan 2012, 13:21
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Hi guys, I am struggling with this one, can anyone help pls? 1/x + 1/y =1 xy=6, then what is the value of x^2 + y^2? 1. 12 2. 16 3. 18 4. 20 5. 24 Thanks!
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Re: Algebra [#permalink]
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19 Jan 2012, 13:29



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Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2? [#permalink]
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19 Jan 2012, 13:34
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Got it! I forgot that a^2 + b^2 = (a+b)^2  2ab!
Thank you



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Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2? [#permalink]
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14 Jul 2014, 21:33
\(\frac{1}{x} + \frac{1}{y} = 1\) x+y = xy Squaring both sides \(x^2 + 2(xy) + y^2 = (xy)^2\) \(x^2 + y^2 = (xy)^2  2(xy)\) Placing value of xy = 6 \(x^2 + y^2 = 36  12 = 24\) Answer = 24
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Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2? [#permalink]
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22 Jul 2015, 00:05
1/x + 1/y = 1; xy = 6. 1/x + 1/y = 1 x+y/xy = 1 x+y/6 = 1 (since xy = 6) so, x+y = 6. x^2+y^2 = (x+y)^2  2xy = (6)^2  2(6) = 36  12 = 24. Ans (E).
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1/x+1/y=1 xy=6, then what is the value of x^2+y^2? [#permalink]
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Updated on: 14 Mar 2016, 04:06
Hi everyone!
How come that x^2 + y^2 equals (x+y)^2  2xy ?
Is it like an algebraic identity formula? I haven't seen this one anywhere.
Thanks!
Originally posted by iliavko on 14 Mar 2016, 04:02.
Last edited by iliavko on 14 Mar 2016, 04:06, edited 1 time in total.



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Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2? [#permalink]
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14 Mar 2016, 04:06
iliavko wrote: Hi everyone!
How come that x^2 + y^2 equals (x+y)^2  2xy ?
Is it like a difference of squares formula? I haven't seen this one anywhere.
Thanks! It comes from rearranging terms in the formula: \((a+b)^2 = a^2+2ab+b^2\) > \(a^2+b^2 = (a+b)^22ab\) Hope this helps.



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1/x+1/y=1 xy=6, then what is the value of x^2+y^2? [#permalink]
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14 Mar 2016, 04:07
Nice!!.. The stuff you discover at this forum Thanks you so much! One more question, maybe it's silly, but.. What about difference of squares? a^2  b^2 = (a+b)(ab) what is the rationale behind it? Any formula that manipulated leads to it? Thank you!



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Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2? [#permalink]
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14 Mar 2016, 04:22
Splendidgirl666 wrote: Hi guys,
I am struggling with this one, can anyone help pls?
1/x + 1/y =1 xy=6, then what is the value of x^2 + y^2?
1. 12 2. 16 3. 18 4. 20 5. 24
Thanks! x*y=6 x+y=6 (x+y)^2=x^2+y^2+2*x*y 36=()+12 Therefore, the answer is 24



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Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2? [#permalink]
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15 Mar 2016, 00:49
Splendidgirl666 wrote: Hi guys,
I am struggling with this one, can anyone help pls?
1/x + 1/y =1 xy=6, then what is the value of x^2 + y^2?
1. 12 2. 16 3. 18 4. 20 5. 24
Thanks! See here => 1/x+1/y=1 so taking the lcm we get => x+y=xy so (x+y)^2 =36 x^2+y^2=362xy=3612 = 24 hence E
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Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2? [#permalink]
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