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# 1/x+1/y=1 xy=6, then what is the value of x^2+y^2?

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Intern
Joined: 29 Sep 2011
Posts: 16
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!
[Reveal] Spoiler: OA
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Posts: 44566

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19 Jan 2012, 13:29
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Expert's post
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!

$$\frac{1}{x}+\frac{1}{y}=1$$ --> $$\frac{x+y}{xy}=1$$ --> $$x+y=xy$$. Since $$xy=6$$ then $$x+y=6$$.

Now, $$x^2+y^2=(x+y)^2-2xy=6^2-2*6=24$$.

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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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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

$$x^2 + y^2 = 36 - 12 = 24$$

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Senior Manager
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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: $$(a+b)^2 = a^2+2ab+b^2$$ ---> $$a^2+b^2 = (a+b)^2-2ab$$

Hope this helps.
Senior Manager
Joined: 08 Dec 2015
Posts: 305
GMAT 1: 600 Q44 V27
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)(a-b) 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
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Joined: 12 Aug 2015
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GRE 1: 323 Q169 V154
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=36-2xy=36-12 = 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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14 Apr 2018, 13:03
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Re: 1/x+1/y=1 xy=6, then what is the value of x^2+y^2?   [#permalink] 14 Apr 2018, 13:03
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