# 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

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.