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

Nithin said: (Feb 5, 2011) | |

(a+b)^{2} + (a-b)^{2} = 2(a^{2} + b^{2}) |

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). |

Naomi Mwamba said: (May 22, 2021) | |

Can someone clearly explain this in step by step? |

Jamshaid said: (Aug 31, 2022) | |

@All. Here, as whatever power of 1, it remains 1, simply; (3)^1/2 +1 = (4)^1/2 = 2; (3)^1/2 - 1 = (2)^1/2, Thereby X = (2)^1/2 & Y = 1/(2)^1/2, X^2 = 2 & Y^2 = 1/2. Ans 2.5. |

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