Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 124)
124.
217 x 217 + 183 x 183 = ?
Answer: Option
Explanation:
| (217)2 + (183)2 | = (200 + 17)2 + (200 - 17)2 |
| = 2 x [(200)2 + (17)2] [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)] | |
| = 2[40000 + 289] | |
| = 2 x 40289 | |
| = 80578. |
Discussion:
4 comments Page 1 of 1.
Queen said:
9 years ago
Why you didn't calculate the square value for 183 instead of (200 - 17)^2?
(1)
Harshita said:
4 years ago
Anyone please explain this shortly.
(2)
Vishal nasit said:
4 years ago
We can simply take a2+b2 = (a+b) (a-b).
= 400 * 34,
= 13600.
= 400 * 34,
= 13600.
(2)
Subin raj said:
1 year ago
Qns: 217 x 217 + 183 x 183.
Let’s take it as (217)2 + (183)2 = a2 + b2.
Hence: 2(a2 + b2) = (a+b)2 +(a-b)2 and it becomes (a2+b2) =[(a+b)2+(a-b)2]/2.
Therefore;
217 x 217 + 183 x 183 = [(217+183)2+(217-183)2]/2
= (4002+342)/2.
=(160000+1156)/2.
= 161156/2 = 80578.
Let’s take it as (217)2 + (183)2 = a2 + b2.
Hence: 2(a2 + b2) = (a+b)2 +(a-b)2 and it becomes (a2+b2) =[(a+b)2+(a-b)2]/2.
Therefore;
217 x 217 + 183 x 183 = [(217+183)2+(217-183)2]/2
= (4002+342)/2.
=(160000+1156)/2.
= 161156/2 = 80578.
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