Aptitude - Numbers - Discussion

Discussion :: Numbers - General Questions (Q.No.35)

35. 

(963 + 476)2 + (963 - 476)2 = ?
(963 x 963 + 476 x 476)

[A]. 1449
[B]. 497
[C]. 2
[D]. 4
[E]. None of these

Answer: Option C

Explanation:

Given Exp. = (a + b)2 + (a - b)2 = 2(a2 + b2) = 2
(a2 + b2) (a2 + b2)

Ayush Sakhare said: (Dec 16, 2015)  
How did you add (a+b)2 & (a-b)2?

Abhishek Guruji said: (Jun 22, 2016)  
(a+b)^2 + (a-b)^2,

a^2 + b^2 + 2ab + a^2 + b^2 - 2ab,

a^2 + b^2 + a^2 + b^2,

2a^2 + 2b^2,

2(a^2+b^2).

Bruce said: (Aug 5, 2016)  
(a + b) ^2 + (a - b) ^2 = 2 (a^2 + b^2).
(a^2 + b^2) = 1/2 [(a + b) ^2 + (a - b) ^2].

Then,
2 (a^2 + b^2) ÷ 1/2[(a + b) ^2 + (a - b) ^2].

Then, 2 * 2/1 = 4.

Why 4 is not an answer? please help me.

Swechha said: (Aug 22, 2018)  
Please, Explain the steps to get the answer.

Kamlesh Bisht said: (Apr 1, 2019)  
a^2+b^2 = 1/2(a+b)^2+(a+b)^2 use this formula.

Ananthu said: (Aug 4, 2021)  
(a+b) ^2+ (a-b) ^2/ (a^2 + b^2) = a^2+b^2+2ab+a^2+b^2-2ab/(a^2 + b^2).

2a^2+2b^2/ (a^2 + b^2) = 2 (a^2+b^2)/(a^2 + b^2) = 2.

Tashi Tshering said: (Aug 5, 2021)  
(a+b)^2 +(a-b)^2.

Since power is 2 is even no. Even though there is -b, it will become positive.
So a^2+b^2+a^2+b^2= 2a^2+2b^2.
Take common one out 2(a^2+b^2)/(a^2+b^2).
Which is exactly divisible by the denominator.

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