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In the equation above, x =
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Bunuel
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In the equation above, x = [#permalink] New post  29 Mar 2017, 01:42
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A
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78% (01:36) correct 22% (01:53) wrong based on 405 sessions

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\(x(5+\sqrt{7})=90\)
In the equation above, x =

A. \(5(5-\sqrt{7})\)

B. 15/2

C. 45

D. \(90(5-\sqrt{7})\)

E. \(90(5+\sqrt{7})\)
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Re: In the equation above, x = [#permalink] New post  29 Mar 2017, 02:20
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Bunuel wrote:
\(x(5+\sqrt{7})=90\)
In the equation above, x =

A. \(5(5-\sqrt{7})\)

B. 15/2

C. 45

D. \(90(5-\sqrt{7})\)

E. \(90(5+\sqrt{7})\)


\(x(5+\sqrt{7}) = 90\)

\(x = 90/(5+\sqrt{7})\)

\(x = (90*(5-\sqrt{7}))/((5+\sqrt{7})*(5-\sqrt{7}))\)

\(x = (90*(5-\sqrt{7}))/(25-7)\)

\(x = (90*(5-\sqrt{7}))/18\)

\(x = 5*(5-\sqrt{7})\)

Hence option A is correct
Hit Kudos if you liked it 8-)
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ScottTargetTestPrep
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Re: In the equation above, x = [#permalink] New post  16 Oct 2018, 17:14
Expert Reply
Bunuel wrote:
\(x(5+\sqrt{7})=90\)
In the equation above, x =

A. \(5(5-\sqrt{7})\)

B. 15/2

C. 45

D. \(90(5-\sqrt{7})\)

E. \(90(5+\sqrt{7})\)


Simplifying we have:

x = 90/(5 + √7)

We must rationalize the denominator by multiplying numerator and denominator of the right side of the equation by the conjugate of (5 + √7). The conjugate of (5 + √7) is (5 - √7). Multiplying the rightside by (5 - √7)/(5 - √7), we have:

90(5 - √7)/(25 - 7) = 90(5 - √7)/18 = 5(5 - √7)

Answer: A
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Re: In the equation above, x = [#permalink] New post  16 Oct 2018, 18:59
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Kudos
The best approach for solving this question is to simply put the answer choices one by one in place of x
By inputing answer choices in value of x, we get Option B as the answer where L.H.S=R.H.S.
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jfranciscocuencag
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Re: In the equation above, x = [#permalink] New post  13 Jan 2019, 15:44
ScottTargetTestPrep wrote:
Bunuel wrote:
\(x(5+\sqrt{7})=90\)
In the equation above, x =

A. \(5(5-\sqrt{7})\)

B. 15/2

C. 45

D. \(90(5-\sqrt{7})\)

E. \(90(5+\sqrt{7})\)


Simplifying we have:

x = 90/(5 + √7)

We must rationalize the denominator by multiplying numerator and denominator of the right side of the equation by the conjugate of (5 + √7). The conjugate of (5 + √7) is (5 - √7). Multiplying the rightside by (5 - √7)/(5 - √7), we have:

90(5 - √7)/(25 - 7) = 90(5 - √7)/18 = 5(5 - √7)

Answer: A


Hello ScottTargetTestPrep !

Why usually when we rationalize the denominator it ends up being 1 but in this case is not?

I have seen a lot of examples here that people automatically put a 1 after this kind of terms:

(5 + √7)(5 - √7) = 1 (Now I know is not 1)

Should we have to solve it in all cases?

Kind regards!
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ScottTargetTestPrep
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Re: In the equation above, x = [#permalink] New post  14 Jan 2019, 18:08
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Hi jfranciscocuencag,

It sometimes ends up as 1; for example, (4 + √15) x (4 - √15) = 16 - 15 = 1; however in other examples the outcome is not 1.

For example, (4 + √14) x (4 - √14) = 16 - 14 = 2. More often, it is the latter case rather than the former, so never expect for the result to be 1 until you carry out the multiplication.
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firas92
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Re: In the equation above, x = [#permalink] New post  31 Jan 2019, 03:36
I had considered that x must be between 90/(5+√9) & 90/(5+√4) [Since working with perfect squares is a lot easier].

Which roughly means 11<x<12

So A is the only option that is even remotely close to this range.

*Is this approach correct?*
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EgmatQuantExpert
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Re: In the equation above, x = [#permalink] New post  28 Feb 2020, 14:08
Expert Reply

Solution



Given
    • x(5+√7)=90

To find
    • Value of x

Approach and Working out
    • x(5+√7)=90
    • x = 90 / (5+√7)
    • Multiplying by (5-√7) in both numerator and denominator, we get:
      o x =90(5-√7)/ (25-7)
      o x =90(5-√7)/ 18
      o x =5(5-√7)

Hence, option A is the correct answer.

Correct Answer: Option A
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Re: In the equation above, x = [#permalink] New post  15 Mar 2021, 00:31
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