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# If x = 1/(√11 + √10) and y =

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CEO
Joined: 12 Sep 2015
Posts: 2561
If x = 1/(√11 + √10) and y = [#permalink]

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01 Mar 2017, 09:08
Top Contributor
3
00:00

Difficulty:

45% (medium)

Question Stats:

70% (01:42) correct 30% (02:32) wrong based on 98 sessions

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If $$x = \frac{1}{√11 + √10}$$ and $$y = \frac{1}{√11 - √10}$$, then what is the value of x² - xy + y²?

A) 39
B) 41
C) 43
D) 45
E) 47

*kudos for all correct solutions

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Brent Hanneson – Founder of gmatprepnow.com

Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
If x = 1/(√11 + √10) and y = [#permalink]

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01 Mar 2017, 09:24
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2
GMATPrepNow wrote:
If $$x = \frac{1}{√11 + √10}$$ and $$y = \frac{1}{√11 - √10}$$, then what is the value of x² - xy + y²?

A) 39
B) 41
C) 43
D) 45
E) 47

*kudos for all correct solutions

Hi

Can't paste a fraction with so many square roots

$$x = \frac{1}{\sqrt{11} + \sqrt{10}} * (\sqrt{11} - \sqrt{10})/(\sqrt{11} - \sqrt{10}) = \sqrt{11} - \sqrt{10}$$

$$y = \frac{1}{\sqrt{11} - \sqrt{10}} * (\sqrt{11} + \sqrt{10})/(\sqrt{11} + \sqrt{10}) = \sqrt{11} + \sqrt{10}$$

$$x^2 - xy + y^2 = (\sqrt{11} - \sqrt{10})^2 - (\sqrt{11} - \sqrt{10})(\sqrt{11} + \sqrt{10}) + (\sqrt{11} + \sqrt{10})^2 =$$
$$11 - 2*\sqrt{11}*\sqrt{10} + 10 - (11 - 10) + 11 + 2*\sqrt{11}*\sqrt{10} + 10 = 41$$

Intern
Joined: 07 Sep 2012
Posts: 8
GMAT 1: 650 Q50 V28
GPA: 2.8
WE: Operations (Retail)
Re: If x = 1/(√11 + √10) and y = [#permalink]

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01 Mar 2017, 09:58
1
x^2-xy+y^2 can be written as (x-y)^2 + xy....plug in the values the solution will simplify correct answer 41

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Joined: 11 Jun 2011
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GPA: 3.5
Re: If x = 1/(√11 + √10) and y = [#permalink]

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01 Mar 2017, 10:46
1
GMATPrepNow wrote:
If $$x = \frac{1}{√11 + √10}$$ and $$y = \frac{1}{√11 - √10}$$, then what is the value of x² - xy + y²?

A) 39
B) 41
C) 43
D) 45
E) 47

*kudos for all correct solutions

$$x^2 = (\frac{1}{√11 + √10})^2$$

Or, $$x^2 = \frac{1}{11 + 10 + 2√110}$$ $$= \frac{1}{21 + 2√110}$$

$$y^2 = (\frac{1}{√11 - √10})^2$$

Or, $$y^2 = \frac{1}{11 + 10 - 2√110}$$ $$= \frac{1}{21 - 2√110}$$

$$xy = \frac{1}{√11 + √10}*\frac{1}{√11 - √10}$$

So, $$xy = \frac{1}{11 - 10}$$ $$= 1$$

Now, $$x^2 - xy + y^2 = \frac{1}{21 + 2√110} - 1 + \frac{1}{21 - 2√110} = 41$$

Thus, answer must be (B) 41
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Abhishek....

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Re: If x = 1/(√11 + √10) and y =   [#permalink] 01 Mar 2017, 10:46
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