If (3 + 2√2)^(x^2 - 3)} + (3 - 2√2)^(x^2 - 3) = 1 which of the followi

Question

Competition Mode Question

If  (3 + 2√2)^{(x^2 - 3)} + (3 - 2√2)^{(x^2 - 3)} = b  which of the following can be the value of b?

A. -1
B. 0
C. 1
D.  \sqrt{2} 
E. 2

Are You Up For the Challenge: 700 Level Questions

nick1816 · Accepted Answer

b=(3+2\sqrt2)^{x^2-3} + (3-2\sqrt2)^{x^2-3}

Also,
 (3+2\sqrt2)*(3-2\sqrt2) = 9-8=1

(3+2\sqrt2) = \frac{1}{(3-2\sqrt2)}

or

(3+2\sqrt2)^{x^2-3} = \frac{1}{(3-2\sqrt2)^{x^2-3}}

Sum of a positive number and it's reciprocal can never be less than 2.

E

firas92 · Answer

If  x=\sqrt3 ,

b=(3+2\sqrt2)^0 + (3-2\sqrt2)^0=1+1=2

Answer is  (E)

Posted from my mobile device

MayankSingh · Answer

IMO E

Let x=√ 3 (Since no information about x is available so we can assume it to be anything)
x^2-3 = 0

(3+2√2)^(x2−3)+(3−2√2)^(x2−3)=b
=> (3+2√2)^0 + (3+2√2)^0 = b
=> 1 + 1 = b
=> b =2

E. 2

unraveled · Answer

If  (3+2√2)^{(x^2−3)} + (3−2√2)^{(x^2−3)} = b  which of the following can be the value of b?

A. -1
B. 0
C. 1
D. √2
E. 2

Since 3+2√2 > 0 & 3-2√2 > 0,  b ≤ 0 . So, b > 0
A and B are out.

As question asks b can take a value out of the five options, we need to find one options that satisfies the condition. 
Hence the easiest solution is when  (xˆ2-3) = 0 (there's no condition for x which can take any value), Thus,  (3+2√2)^{(x^2−3)}  = 1 and 
 (3-2√2)^{(x^2−3)}  = 1 also

So,  (3+2√2)^{(x^2−3)} + (3+2√2)^{(x^2−3)} = 1+1 = 2

Answer E. 
 Note: Many answers are possible i.e. b can take any value depending the value we consider for 'x' but since 2 is available as answer and in PS only one option is correct, we need to bother whether C and D are correct.

HoneyLemon · Answer

Is it E ?

If (3+2√2)^(x^2−3)+(3−2√2)^(x^2−3)=b
 which of the following can be the value of b?

if x^2−3 = 0 then total expression can be 
 (3+2√2)^(0)+(3−2√2)^(0)= 1 + 1 = 2 . 
Hence E .

sambitspm · Answer

Either you can go ahead and start solving forgo with a smart approach.
Put x = sqrt(3)
so x^2-3 = 0

the equation is reduced to (....)^0 + (.....)^0 = 1+1 =  2

exc4libur · Answer

if x=√3, then (..)^0+(..)^0=1+1=2=b

ans (E)

Abi1995 · Answer

We have to concentrate on value of x2-3, this equals to 0, when x=+_/3, with this both x + Y = 1+1= 2= b

So answer is E

Posted from my mobile device

NitishJain · Answer

IMO E.

Lets consider the equation of the form (p+q)^r + (p-q)^r = b

As the Lets try with r= 0, 1

r=0 (i.e. x= sqrt(3)): we get 1 + 1 = b = 2 (which is in the options)
So that is the answer.

If that would not have been among the options, putting r=1; b = 6.

Looking forward to other solutions

monikakumar · Answer

(a+c)^d+(a-c)^d
we can have d=2,1,0...
x^2-3=1,
x=+2,-2
but , when d=1, b=6
when d=0, b=2

In the question they are asking can be the value of b, so 2 can be the value

Ans E

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

If (3 + 2√2)^(x^2 - 3)} + (3 - 2√2)^(x^2 - 3) = 1 which of the followi

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 (3 + 2√2)^(x^2 - 3)} + (3 - 2√2)^(x^2 - 3) = 1 which of the followi

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