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15 Apr 2020, 09:44
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
52% (02:35) correct
48%
(02:35)
wrong
based on 217
sessions
History
Date
Time
Result
Not Attempted Yet
What is the closest integer to the value of the expression:
\(\frac{(2018√2018) -1}{2018 + (√2018) + 1\\
}\)
(A) 36
(B) 38
(C) 40
(D) 42
(E) 44
\(\frac{(2018√2018) -1}{2018 + (√2018) + 1\\
}\)
(A) 36
(B) 38
(C) 40
(D) 42
(E) 44
15 Apr 2020, 10:05
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\(\frac{(2018√2018) -1}{2018 + (√2018) + 1}\)
= \(\frac{(√2018)^3 -1}{(√2018)^2 + (√2018) + 1}\)
\(a^3-b^3 = (a-b)(a^2+b^2+ab)\)
\(\frac{a^3-b^3}{(a^2+b^2+ab) }= (a-b)\)
\(\frac{(√2018)^3 -1^3}{(√2018)^2 + (√2018)*1 + 1^2}\) = (√2018) -1 ≈ 45-1 =44
= \(\frac{(√2018)^3 -1}{(√2018)^2 + (√2018) + 1}\)
\(a^3-b^3 = (a-b)(a^2+b^2+ab)\)
\(\frac{a^3-b^3}{(a^2+b^2+ab) }= (a-b)\)
\(\frac{(√2018)^3 -1^3}{(√2018)^2 + (√2018)*1 + 1^2}\) = (√2018) -1 ≈ 45-1 =44
Ravixxx
General Discussion
15 Apr 2020, 10:25
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Ravixxx
What is the closest integer to the value of the expression:
\(\frac{(2018√2018) -1}{2018 + (√2018) + 1\\
}\)
a^3 - 1 = (a-1)(a^2 +a + 1)
If a = √2018
2018√2018) -1 = (√2018 -1)(2018 + (√2018) + 1)
\(\frac{(2018√2018) -1}{2018 + (√2018) + 1\\
}=√2018 -1 ~ 45-1 =44 \)
IMO E
