Aptitude - Surds and Indices - Discussion

Discussion :: Surds and Indices - General Questions (Q.No.15)

15. 

If x = 3 + 22, then the value of x - 1 is:
x

[A]. 1
[B]. 2
[C]. 22
[D]. 33

Answer: Option B

Explanation:

x - 1 2 = x + 1 - 2
x x

   = (3 + 22) + 1 - 2
(3 + 22)

   = (3 + 22) + 1 x (3 - 22) - 2
(3 + 22) (3 - 22)

   = (3 + 22) + (3 - 22) - 2

   = 4.

x - 1 = 2.
x


Ravi said: (Dec 26, 2010)  
How the value of the (3-2 2)(3+2 2)=1?
Here "2 2" means what ?

Aparna said: (Jan 28, 2011)  
@ravi,

Your prblm is how the denominator part came 1
see
the denominator is
(3-2 2)(3+2 2)
use the formula
(a+b)(a-b)=a2(square)-b2(square)
hence
3(square)-(2(square)*2)
here suqreroot of one 2 gets removed
we get
9-8=1

Shahid said: (May 20, 2011)  
Convert the expression x into (a+b)^2 form

with a=squareroot(2) and b=1

and then after that try it

Preethi said: (Sep 23, 2011)  
Can anyone explain this sum clearly? please.

Hari said: (Oct 16, 2011)  
There is no power of 2 at all. How would you get the answer ?

Neenu said: (Dec 8, 2011)  
x= 3+ 2(root)2
=> 2+1+2(root)2.(root)1
{which is} [(root)2+1)^2
hence, (root)x=(root)2+1
1/(root)x=1/(root)2+1 => (root)2-1

So when we add them [x+1/(root)x] = (root)2+1-[(root)2-1]=>(root)2+1-(root)+1=>2

Saroj said: (Jan 18, 2012)  
Please explain the logic behind step-3.

Anuradha said: (Feb 27, 2012)  
Its same as (a-b)^2 formula.

Sagar Sharma said: (Mar 6, 2012)  
The answer should have been 1. As we put the value of x in given expression and rationalize 1/x, we get 1 as the answer.

Sagar Jain said: (Apr 9, 2012)  
What if we have to find out x^4 +x^ (-4).

Varun said: (Apr 10, 2012)  
Question is to find (x^1/2 - 1/x^1/2)
Then there is square in the explanations first line.

Vicky said: (Apr 10, 2012)  
Question is to find (x^1/2 - 1/x^1/2).
Then why there is square in the explanations first line.
Why?

Hima said: (Aug 8, 2012)  
3+2(root)2 can be written as 1+2(1)(root2)+ (root2)^2 which is equal to (1+root2)^2 [a^2+b^2+2ab=(a+b)^2].
So
Now x=(1+root2)^2 now put this value in the question.

Swetha said: (Aug 31, 2013)  
Can anyone please explain whole sum clearly how -2 came in the 2nd step of the sum?

Gaurav Bhardwaj said: (Sep 3, 2013)  
@Swetha.

If you will square that term using formulae (a-b)^2 = a^2+b^2-2ab, then you will automatically come to know how -2 came in second step.

Joe said: (Oct 4, 2013)  
In first step, where did minus 2 come from ?

Sefah said: (Mar 16, 2014)  
How do we get the square in the 1st step because it wasn't part of the question?

Gayathri said: (Apr 19, 2014)  
Here given 'x' value only not root 'x'. So answer is 2(1+root2).

Nicky said: (Sep 27, 2015)  
Why we subtract -2 in 1st step?

Srinivas said: (Feb 16, 2016)  
4th step is the problem. Where did the denominator go. No proper explanation.

Ahmed said: (Mar 2, 2016)  
Actual answer is 4, but why should be 2.

Suma said: (Mar 11, 2016)  
Answer is 4 how do you get 2?

Vijay said: (Jul 20, 2016)  
Please explain how they take ^2over it?

Priyanka said: (Jul 30, 2016)  
Why -2 is wriiten at the end ? From where it came ?

Rohit said: (Aug 3, 2016)  
Answer is 4 how do you get 2?

Raja Raviteja said: (Sep 2, 2016)  
^2 = 1.414.
3 + 2^2 = 5.828. Where ^x = ^5.818 = 2.414.

So, ^x - 1/^x = 2.414 - (1/2.414) = 2 =>answer.

Priyanka said: (Oct 10, 2016)  
Not getting this, can anyone explain clearly?

Harshini said: (Dec 20, 2016)  
In the 4th step, if you see the denominator: (a+b) (a-b) = (a^2-b^2) (using the formula).
It becomes 3^2 -(2 root 2)^2.
Which is 9 - (4 * 2),
=> 9 - 8 = 1.

Saurav Kumar said: (Feb 10, 2017)  
If x+1/x =1 then (x+1)^3 + 1/(x+1)^3 = ?

Please solve it.

Valens said: (Feb 15, 2017)  
How 4 = 2 at last?

Felix said: (Mar 13, 2017)  
How did you obtain 1/x +x -2?

Akashdeep Singh said: (May 20, 2017)  
In the last stage where we find the value of [(underoot)x - 1/(underoot)x]^2 = 4.

So if you remove the square then it will become (underoot)4 i.e. 2.
(underoot)x - 1/(underoot)x = (underoot)4.
(underoot)x - 1/(underoot)x = 2.

Bishal Dey said: (Jul 25, 2017)  
= 3+2√2 + 1/3+2√2 -2,
= 3+2√2 + 3 - 2√2 -2,
=6-2.
=4.
=√4=2.

Harigovind C B said: (Sep 11, 2017)  
if a÷b=4÷5 and b÷c=15÷16 , then (c^2-a^2)÷c^2+a^2 is equal to?

Can anyone solve this?

Mahima said: (Sep 23, 2017)  
4th step how to solve the denominator (3+2√2)(3-2√2)? Please explain.

Bfc said: (Jun 13, 2018)  
How to solve 4th step the denominator (3+2√2) (3-2√2)? Please explain.

Milind said: (Jan 23, 2019)  
(√x-1/√) -2 = (x + 1/x) - 2.

Can you tell me where this -2 comes from?

Mohan said: (May 26, 2019)  
@Joe.

In the first step, it is in the form of (a-b) ^2 formula.

Post your comments here:

Name *:

Email   : (optional)

» Your comments will be displayed only after manual approval.