If (2 - sqrt(5))x = -1, then x =

Question

If  (2-\sqrt{5})x = -1 , then  x=

A.  2 + \sqrt{5}

B.  1 + \frac{\sqrt{5}}{2}

C.  1 - \frac{\sqrt{5}}{2}

D.  2 - \sqrt{5}

E.  -2 - \sqrt{5}

Bunuel · Answer

If  (2-\sqrt{5})x = -1 , then  x= ?

A.  2 + \sqrt{5}

B.  1 + \frac{\sqrt{5}}{2}

C.  1 - \frac{\sqrt{5}}{2}

D.  2 - \sqrt{5}

E.  -2 - \sqrt{5}

(2-\sqrt{5})x = -1  -->  x=-\frac{1}{2-\sqrt{5}}=\frac{1}{\sqrt{5}-2} . Multiply both denominator and nominator by  \sqrt{5}+2 :

x=\frac{\sqrt{5}+2}{(\sqrt{5}-2)(\sqrt{5}+2)}=\frac{\sqrt{5}+2}{\sqrt{5}^2-2^2}=\frac{\sqrt{5}+2}{5-4}=\sqrt{5}+2 .

Answer: A.

144144 · Answer

Geez, i feel stupid.... explain me plz the following stages:
1. x=-\frac{1}{2-\sqrt{5}}=\frac{1}{\sqrt{5}-2}
2. the last stage.

Thanks for ur time.

PareshGmat · Answer

(2 - \sqrt{5}) x = -1

x = \frac{1}{\sqrt{5} - 2}

Multiple RHS numerator & denominator by  \sqrt{5} + 2

x = \frac{\sqrt{5} + 2}{(\sqrt{5} + 2) (\sqrt{5} - 2)}

x = \frac{\sqrt{5} + 2}{5-4}

x = \sqrt{5} + 2

Answer = A

Abhibarua · Answer

(2 - sqrt(5))x = -1

Let's multiply both sides by (2 + sqrt(5)):

(2 - sqrt(5)) (2 + sqrt(5))x = -1(2 + sqrt(5))

(4-5)x = -1(2 + sqrt(5))

x = (2 + sqrt(5))

ramlala · Answer

(2-\sqrt{5})x = -1

x = \frac{-1}{(2-\sqrt{5})}

x = \frac{-1}{(2-\sqrt{5})} * \frac{(2+\sqrt{5})}{(2+\sqrt{5})}

x = \frac{-1 (2+\sqrt{5})}{(4-5)}

x = \frac{-1 (2+\sqrt{5})}{(-1)}

x = 2+\sqrt{5}

Ans A

v12345 · Answer

(2-\sqrt{5})x = -1 
 x =\frac{ -1}{(2-\sqrt{5})}

Rationalizing the denominator,  we get
 x =\frac{ -1(2+\sqrt{5})}{(4-5)}   = 2+\sqrt{5}

Hence, OA is (A).

BrushMyQuant · Answer

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧

https://www.youtube.com/watch?v=1_5K_O-EphU

Given that  (2-\sqrt{5})x  = -1 and we need to find the value of x

(2-\sqrt{5})x  = -1
=> x =  \frac{-1}{2-\sqrt{5} }  =  \frac{1 }{ \sqrt{5} - 2}

Multiplying numerator and denominator with  \sqrt{5} + 2  we get

x =  \frac{1 * \sqrt{5} + 2}{ (\sqrt{5} - 2)*(\sqrt{5} + 2)} 
=  \frac{\sqrt{5} + 2}{(\sqrt{5})^2 - 2^2}  =  \frac{\sqrt{5} + 2}{5 - 4}  =  \sqrt{5} + 2

So,  Answer will be A 
Hope it helps!

Watch the following video to learn How to Rationalize Roots

https://www.youtube.com/watch?v=LhR_gXt8CLw

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If (2 - sqrt(5))x = -1, then x =

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If (2 - sqrt(5))x = -1, then x =

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards