It is currently 23 Jan 2018, 10:07

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x-5=x+5 , x=?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4715
GPA: 3.82

### Show Tags

12 Sep 2017, 01:11
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

67% (01:42) correct 33% (02:33) wrong based on 79 sessions

### HideShow timer Statistics

If $$x-5=\sqrt{x}+\sqrt{5}$$ , x=?

A. $$6+2\sqrt{5}$$
B. $$6-2\sqrt{5}$$
C. $$6+\sqrt{5}$$
D. $$6-\sqrt{5}$$
E. $$5+2\sqrt{6}$$
[Reveal] Spoiler: OA

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Senior Manager
Joined: 02 Jul 2017
Posts: 287
GMAT 1: 730 Q50 V38
Re: If x-5=x+5 , x=? [#permalink]

### Show Tags

12 Sep 2017, 02:44
2
This post was
BOOKMARKED
Given: $$x-5 = \sqrt{x} + \sqrt{5}$$

=> $$(\sqrt{x})^2 - (\sqrt{5})^2 = \sqrt{x} + \sqrt{5}$$
=> $$(\sqrt{x} + \sqrt{5})(\sqrt{x} - \sqrt{5}) = \sqrt{x} + \sqrt{5}$$
=> $$(\sqrt{x} - \sqrt{5}) = (\sqrt{x} + \sqrt{5}) / (\sqrt{x} + \sqrt{5})$$
=>$$(\sqrt{x} - \sqrt{5}) = 1$$
=> $$\sqrt{x} = \sqrt{5} + 1$$

Squaring both sides
=>$$x= 1+5 +2*1* \sqrt{5}$$
=>$$x= 6+2\sqrt{5}$$

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4715
GPA: 3.82
Re: If x-5=x+5 , x=? [#permalink]

### Show Tags

13 Sep 2017, 23:55
=>
x-5=√x+√5
(√x+√5)(√x-√5)=√x+√5
√x-√5 = 1
√x = 1+√5
x = 1 + 2√5 + 5 = 6 + 2√5

Ans: A
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Intern
Status: Enjoying the Journey
Affiliations: Toronto
Joined: 08 Jan 2017
Posts: 26
ND: SS
Schools: Rotman '21
WE: Marketing (Consulting)
Re: If x-5=x+5 , x=? [#permalink]

### Show Tags

16 Sep 2017, 22:52
MathRevolution wrote:
=>
x-5=√x+√5
(√x+√5)(√x-√5)=√x+√5
√x-√5 = 1
√x = 1+√5
x = 1 + 2√5 + 5 = 6 + 2√5

Ans: A

I tried to square both sides but it didn't work, I don't understand why, is it wrong to square both sides

x-5=√x+√5 ...by squaring both sides
(x-5)^2= (√x+√5)^2
(x-5)(x+5)=(x+5)+2√x√5
(x-5)= 1+2√x√5
x= 1+2√x√5+5
x=6+2√x√5

Can someone help me to find what I did wrong, thx
_________________

High achievement always takes place in the framework of high expectation Charles Kettering
If we chase perfection we can catch excellence Vince Lombardi

Using Forum Tags: https://gmatclub.com/forum/using-forum-tags-158411.html#p1909410

Senior Manager
Joined: 02 Jul 2017
Posts: 287
GMAT 1: 730 Q50 V38
Re: If x-5=x+5 , x=? [#permalink]

### Show Tags

16 Sep 2017, 23:21
1
KUDOS
NNDD wrote:
MathRevolution wrote:
=>
x-5=√x+√5
(√x+√5)(√x-√5)=√x+√5
√x-√5 = 1
√x = 1+√5
x = 1 + 2√5 + 5 = 6 + 2√5

Ans: A

I tried to square both sides but it didn't work, I don't understand why, is it wrong to square both sides

x-5=√x+√5 ...by squaring both sides
(x-5)^2= (√x+√5)^2
(x-5)(x+5)=(x+5)+2√x√5
(x-5)= 1+2√x√5
x= 1+2√x√5+5
x=6+2√x√5

Can someone help me to find what I did wrong, thx

x-5=√x+√5 ...by squaring both sides
(x-5)^2= (√x+√5)^2
(x-5)(x+5)=(x+5)+2√x√5 => Here you used wrong formula, =>$$(a-b)^2 = a^2+b^2-2ab$$ and $$a^2 -b^ 2 = (a-b)(a+b)$$
Here after squaring correct expansion is :
(x-5)^2= (√x+√5)^2
$$x^2+25-2*25*x$$= $$(x+5)+2\sqrt{x}\sqrt{5}$$
$$x^2+25-50x = x+5+2\sqrt{x}\sqrt{5}$$
Intern
Status: Enjoying the Journey
Affiliations: Toronto
Joined: 08 Jan 2017
Posts: 26
ND: SS
Schools: Rotman '21
WE: Marketing (Consulting)
Re: If x-5=x+5 , x=? [#permalink]

### Show Tags

17 Sep 2017, 01:15
1
KUDOS
Nikkb wrote:
NNDD wrote:
MathRevolution wrote:
=>
x-5=√x+√5
(√x+√5)(√x-√5)=√x+√5
√x-√5 = 1
√x = 1+√5
x = 1 + 2√5 + 5 = 6 + 2√5

Ans: A

I tried to square both sides but it didn't work, I don't understand why, is it wrong to square both sides

x-5=√x+√5 ...by squaring both sides
(x-5)^2= (√x+√5)^2
(x-5)(x+5)=(x+5)+2√x√5
(x-5)= 1+2√x√5
x= 1+2√x√5+5
x=6+2√x√5

Can someone help me to find what I did wrong, thx

x-5=√x+√5 ...by squaring both sides
(x-5)^2= (√x+√5)^2
(x-5)(x+5)=(x+5)+2√x√5 => Here you used wrong formula, =>$$(a-b)^2 = a^2+b^2-2ab$$ and $$a^2 -b^ 2 = (a-b)(a+b)$$
Here after squaring correct expansion is :
(x-5)^2= (√x+√5)^2
$$x^2+25-2*25*x$$= $$(x+5)+2\sqrt{x}\sqrt{5}$$
$$x^2+25-50x = x+5+2\sqrt{x}\sqrt{5}$$

Thanks a lot for explaining this, this a serious misconception from me, appreciate it

I now realized that this can't be solved by squaring both sides, as it gave complicated calculations and more square roots...How can we decide which path we go ...squaring both sides versus simplifying one side as it was shown in the provided answer

Thanks,
NNDD
_________________

High achievement always takes place in the framework of high expectation Charles Kettering
If we chase perfection we can catch excellence Vince Lombardi

Using Forum Tags: https://gmatclub.com/forum/using-forum-tags-158411.html#p1909410

Senior Manager
Joined: 02 Jul 2017
Posts: 287
GMAT 1: 730 Q50 V38
Re: If x-5=x+5 , x=? [#permalink]

### Show Tags

17 Sep 2017, 01:37
1
KUDOS
NNDD wrote:

Thanks a lot for explaining this, this a serious misconception from me, appreciate it

I now realized that this can't be solved by squaring both sides, as it gave complicated calculations and more square roots...How can we decide which path we go ...squaring both sides versus simplifying one side as it was shown in the provided answer

Thanks,
NNDD

You will get used to such type of questions with practice.
Generally everyone initially go with squaring option. We are used to work with integers so we start with expanding in integer format. But after solving few such questions you can used to square roots and formulas related to them
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1835
Re: If x-5=x+5 , x=? [#permalink]

### Show Tags

18 Sep 2017, 04:47
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
MathRevolution wrote:
If $$x-5=\sqrt{x}+\sqrt{5}$$ , x=?

A. $$6+2\sqrt{5}$$
B. $$6-2\sqrt{5}$$
C. $$6+\sqrt{5}$$
D. $$6-\sqrt{5}$$
E. $$5+2\sqrt{6}$$

The key to solving this problem is recognizing that (x - 5) can be expressed as a difference of squares. Recall that an expression like (x^2 - 36), a difference of squares, can be factored as (x - 6)(x + 6). In a similar way, we can factor x - 5 as (√x + √5)(√x - √5). Thus, we have:

(√x + √5)(√x - √5) = √x + √5

Dividing both sides by (√x + √5), since it can’t be 0, we have:

√x - √5 = 1

√x = 1 + √5

x = (1 + √5)^2

x = 1 + 2√5 + 5

x = 6 + 2√5

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If x-5=x+5 , x=?   [#permalink] 18 Sep 2017, 04:47
Display posts from previous: Sort by