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17 Mar 2020, 05:13
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C
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Difficulty:
5%
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Question Stats:
91% (01:06) correct
9%
(01:06)
wrong
based on 74
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What is the sum of 9,999^2 and 10,001^2?
(A) 99,980,001
(B) 199,999,998
(C) 200,000,002
(D) 399,999,996
(E) 400,000,004
(A) 99,980,001
(B) 199,999,998
(C) 200,000,002
(D) 399,999,996
(E) 400,000,004
17 Mar 2020, 05:16
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Bunuel
What is the sum of 9,999^2 and 10,001^2?
(A) 99,980,001
(B) 199,999,998
(C) 200,000,002
(D) 399,999,996
(E) 400,000,004
(A) 99,980,001
(B) 199,999,998
(C) 200,000,002
(D) 399,999,996
(E) 400,000,004
Let \(a = 10,000 = 10^4\)
So, \(9,999^2 + 10,001^2 = (a - 1)^2 + (a + 1)^2\)
= \(a^2 - 2a + 1 + a^2 + 2a + 1\)
= \(2a^2 + 2\)
= \(2(10^4)^2 + 2\)
= \(200,000,002\)
Option C
17 Mar 2020, 05:19
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Bunuel
What is the sum of 9,999^2 and 10,001^2?
(A) 99,980,001
(B) 199,999,998
(C) 200,000,002
(D) 399,999,996
(E) 400,000,004
(A) 99,980,001
(B) 199,999,998
(C) 200,000,002
(D) 399,999,996
(E) 400,000,004
(10,000-1)^2 + (10,000+1)^2 = (10,000^2 -20,000 + 1) + (10,000^2 +20,000 + 1) = 100,000,001 *2 = 200,000,002
IMO C
