Aptitude - Square Root and Cube Root - Discussion

Discussion :: Square Root and Cube Root - General Questions (Q.No.7)

7. 

If x = 3 + 1 and y = 3 - 1 , then the value of (x2 + y2) is:
3 - 1 3 + 1

[A]. 10
[B]. 13
[C]. 14
[D]. 15

Answer: Option C

Explanation:

x = (3 + 1) x (3 + 1) = (3 + 1)2 = 3 + 1 + 23 = 2 + 3.
(3 - 1) (3 + 1) (3 - 1) 2

y = (3 - 1) x (3 - 1) = (3 - 1)2 = 3 + 1 - 23 = 2 - 3.
(3 + 1) (3 - 1) (3 - 1) 2

x2 + y2 = (2 + 3)2 + (2 - 3)2

   = 2(4 + 3)

   = 14


Nithin said: (Feb 5, 2011)  
(a+b)2 + (a-b)2 = 2(a2 + b2)

Gaurav said: (Apr 11, 2011)  
Asnwer to this seems to be '-10'.

Tank Mayur B. said: (Aug 17, 2011)  
This is wrong solution .
because: ((a+b)/(a-b))*((a+b)/(a+b))=(a+b)2/(a2 + b2)

M.V.Krishna/Palvoncha said: (Sep 11, 2011)  
Hello gaurav and tank mayur.

This is the process of rationalization.

The denominator is multiplied and divided to selected value.

Hope you understand.

Mayur said: (Oct 4, 2011)  
Hello M.V.Krishna
You are absolutely right
Thank you....

Yogendra said: (Oct 14, 2011)  
This can also be solvein this formula: (A+B)2 =(a+b)2-2ab

Raje said: (Nov 19, 2011)  
Its called conjugate . + in denominoter means u have to multiply & divide the same number but put - sign. denominoter - sign means put + vice versa.

Shyam said: (Dec 11, 2011)  
Rationalizing the denominator. Makes it very easy and find xy.

Anjani said: (Jan 6, 2012)  
We can do help from the equation (x2+y2)=(x+y)2-2xy;

Priya said: (Mar 3, 2012)  
How did we get 2(4+3) ???

Samart Boy said: (May 31, 2012)  
(2 + 3)2 + (2 - 3)2

= 2(4 + 3) ?

Can you explain?

Jagu said: (Jun 15, 2012)  
How did we get 2(4+3) ?

Bhavesh Joshi said: (Jul 13, 2012)  
Is there any shortcut method to solve ?

Mahesh said: (Jul 30, 2012)  
Hello priya and jaggu ,we can get 2(4+3) as follows:

(a+b)2+(a-b)2=2(a+b).................(1)

Let us prove this

Take LHS of eq(1)

a2+b2+2ab+a2+b2-2ab

Here +2ab and -2ab get cancelled and the remaining can be written as

2a2+2b2

2(a2+b2)


So here a=2 and b=rt3

2(4+3)

Mohit said: (Sep 14, 2012)  
Can any buddy help me to understand this problem solution in a simple and detail way.

Sakthi said: (Jan 10, 2013)  
Root 3 -> 1.732.

1.732+1=2.732.
1.732-1=0.732.

2.732/0.732=3.7322.
0.732/2.732=0.2679.

(3.7322)^2=13.929 & (0.2679)^2=0.0192.

Add 13.929+0.0192=13.9482 is near by 14.

So answer is 14.
Are you clear now friends.

Rizy said: (Oct 14, 2013)  
Solve by the normal method using formula,

(a+b)2 = a2 + 2ab + b2.

(a-b)2 = a2 - 2ab + b2.

By using this formula you will get,

8 + 6 = 14.

Abhinav said: (Jul 15, 2014)  
What if we keep the value of root 3 and proceed? the answer will be 10.

Jessi said: (Jul 20, 2014)  
x = 3*2+1/3-1 = 9+1/2 = 10/2 = 5.

y = 3*2-1/3+1 = 9-1/4 = 8/4 = 2.

The use the formula x2+y2 = 5*2+2*2 = 10+4 = 14.

Kapil said: (Aug 30, 2014)  
Use:

x^2+y^2 = (x+y)^2 - 2xy.

Rajnish Jais said: (Nov 15, 2014)  
Since (x+y)^2-2xy = x^2+y^2.

x+y = 4, 2xy = 1.

Therefore, x^2+y^2 = 14.

Jay said: (Dec 2, 2014)  
Who got 2 as the correct answer? That's what I had and I'm sure I am right!

Chotu said: (Jan 7, 2015)  
(a+b)2+(a-b)2 = 2(a2+b2).

Here a = 2 =>a2 = 4; b = 3^(1/2) =>b2 = 3.

=>2(4+3).

=>2(7).

=>14.

I think this is the correct one because this is the model of rationalization. If this is not the correct answer please explain.

How would you get the answer as 2?

Vipin Kumar said: (Jan 17, 2015)  
How came x = 2+3 and y = 2-3?

Vikas said: (May 17, 2015)  
Could understand how {(3+2)/(3-2) }*{ (3+2)/(3+2)/(3+2)} = (3+2)^2/ (3-2), isn't it should be (3+2)^2/(3^2-1^2)? Please inform me asap.

Gopi said: (Jun 16, 2015)  
The answer is to its formula (x+y)^2=x^2+y^2+2xy.

Abhirup said: (Sep 26, 2015)  
The answer to this question is correct. They have just step-jumped.

Animesh said: (Nov 19, 2015)  
Use "(x^2+y^2) = (x+y)^2-2xy".

Here xy = 1;

Here just put the values of x and y and you can get the answer which is 14.

Jayshree said: (Nov 25, 2015)  
Hello, I just didn't understand how is 3+1+2√3/2 = 2+√3.

Please explain.

Bhavesh Kirange said: (Nov 28, 2015)  
@Jayshree.

3+1 = 4 so it becomes, 4+2√3/2.

Here take 2 common and it comes (2(2+√3))/2 = 2+√3.

Skrn said: (Jan 11, 2016)  
The question I got didn't have a root 3 value. Thanks.

Karthi said: (Aug 8, 2016)  
How to solve this problem logically?

Deepak Gehlot said: (Sep 4, 2016)  
This is wrong solution.

Pranay Patil said: (Nov 14, 2016)  
Can anyone explain me why can't we solve x and y individually to get x^2 = 4 and y^2 = 1/4? So to get x^2 +y^2 = 17/4.

Shudipta Baruah said: (Feb 6, 2017)  
This is correct: 14

x = (3 + 1) x (3 + 1) = (3 + 1)2
= 3 + 1 + 23 = 2 + 3.
(3 - 1) (3 + 1) (3 - 1) 2.

y = (3 - 1) x (3 - 1) = (3 - 1)2 = 3 + 1 - 23 = 2 - 3.
(3 + 1) (3 - 1) (3 - 1) 2,
x2 + y2 = (2 + 3)2 + (2 - 3)2,
= 2(4 + 3),
= 14.

Kalesha said: (Feb 9, 2017)  
(2 + 3) 2 + (2 - 3) 2.
2 (4 + 3).

How can anyone explain this?

Ram said: (Sep 4, 2017)  
(2 + 3) 2 + (2 - 3) 2.

Explanation:
7+4root3+3+4-root3+3.
+4root3-4root3 cancel.

After that,

4+3+4+3 = 14.

Sinthu said: (Sep 28, 2017)  
I couldn't understand. How is it possible?

Sinku said: (Oct 3, 2017)  
x2+y2=(x-y)2+2xy, can we use this formula?

Anyone explain me.

Naren said: (Oct 11, 2017)  
Here, 2(x^2+y^2) = (x+y)^2+(x+y)^2.

Bhushan said: (Mar 18, 2019)  
x2 + y2 = (2 + √3)2 + (2 - √3)2.
= (4+2*2*√3+3) + (4 - 2*2*√3+3),
= (4+3) + (4+3),
= 2(4+3).

Post your comments here:

Name *:

Email   : (optional)

» Your comments will be displayed only after manual approval.