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If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y?

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MathRevolution
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If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y? [#permalink] If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y?   Updated on: 21 May 2020, 09:24
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[GMAT math practice question]

If \(x = \frac{\sqrt{3}-2}{\sqrt{3}+ 2} , y = \frac{\sqrt{3} + 2}{\sqrt{3} - 2}\), what is \(\frac{x^3 + y^3 + 14xy}{x + y}\)?

A. \(172\)

B. \(192\)

C. \(201\)

D. \(213\)

E. \(225\)
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B

Originally posted by MathRevolution on 20 May 2020, 04:10.
Last edited by MathRevolution on 21 May 2020, 09:24, edited 1 time in total.
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yashikaaggarwal
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Re: If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y? [#permalink] If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y?   20 May 2020, 05:14
Sir I checked thrice.
But putting values of x and Y in equation is giving answer around 250+
Kindly verify the options.
Thank You

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MathRevolution
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Re: If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y? [#permalink] If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y?   21 May 2020, 09:25
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yashikaaggarwal wrote:
Sir I checked thrice.
But putting values of x and Y in equation is giving answer around 250+
Kindly verify the options.
Thank You

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There is a mistake in the expression of the variable \(x\).
Sorry about that.
It is fixed now.
Thank you for your comments.
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Re: If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y? [#permalink] If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y?   21 May 2020, 10:44
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Could someone please add a solution to this problem?
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yashikaaggarwal
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Re: If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y? [#permalink] If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y?   21 May 2020, 11:06
Try solving using approximation.
X = √3-2/√3+2 and Y = √3+2/√3-2
Use √3= 1.73
X= -(0.27)/3.73 and Y will be 3.73/-(0.27)
X= -0.072 and Y will be -13.82

Putting values in the equation
X^3+Y^3+14XY/X+Y

=>> (-0.072)^3+(-13.82)^3+14*(-0.072)(-13.81)/-0.072-13.81
=>> -0.000343-2639.52+13.93/13.892
=>> 190 (approx)

Since 190 is the closest approximation to 192. Hence B is the answer.

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If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y? [#permalink] If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y?   21 May 2020, 11:11
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\(x = \frac{\sqrt{3}-2}{\sqrt{3}+ 2} * \frac{\sqrt{3}-2}{\sqrt{3}-2}\)

\(x= 4√3-7 \)

\(y = \frac{\sqrt{3}+2}{\sqrt{3}- 2} * \frac{\sqrt{3}+2}{\sqrt{3}+2}\)

\(y= -7-4√3\)

\(x+y = -14\)

Also, \(x*y=1\)

\((x^2+y^2)= (x+y)^2 - 2xy = 196-2 =194\)

\(x^3+y^3 = (x+y) (x^2+y^2-xy)= -14*(194-1) = -14*193\)

\(x^3+y^3+14xy = -14*193 + 14*1 = 14*(-193+1) = -14*192\)


\(\frac{x^3 + y^3 + 14xy}{x + y}\) \(= \frac{-14*192}{-14} = 192\)



MathRevolution wrote:
[GMAT math practice question]

If \(x = \frac{\sqrt{3}-2}{\sqrt{3}+ 2} , y = \frac{\sqrt{3} + 2}{\sqrt{3} - 2}\), what is \(\frac{x^3 + y^3 + 14xy}{x + y}\)?

A. \(172\)

B. \(192\)

C. \(201\)

D. \(213\)

E. \(225\)
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Re: If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y? [#permalink] If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y?   22 May 2020, 06:27
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Re: If x = 3 -23 + 2, y = 3 + 23 - 2, what is x3 + y3 + 14xyx + y? [#permalink]
22 May 2020, 06:27
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