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18 Mar 2020, 02:24
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C
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Difficulty:
25%
(medium)
Question Stats:
75% (01:38) correct
25%
(01:49)
wrong
based on 633
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If x is positive, what is the least possible value of \(\frac{x}{2} + \frac{2}{x}\)?
(A) 1/2
(B) 1
(C) 2
(D) 3
(E) 4
Are You Up For the Challenge: 700 Level Questions
(A) 1/2
(B) 1
(C) 2
(D) 3
(E) 4
Are You Up For the Challenge: 700 Level Questions
18 Mar 2020, 03:20
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AM ≥ GM
\((\frac{x}{2} + \frac{2}{x})/2 ≥ \sqrt{\frac{x}{2}*\frac{2}{x}}\)
\((\frac{x}{2} + \frac{2}{x})/2 ≥ 1\)
\((\frac{x}{2} + \frac{2}{x}) ≥ 2\)
C
\((\frac{x}{2} + \frac{2}{x})/2 ≥ \sqrt{\frac{x}{2}*\frac{2}{x}}\)
\((\frac{x}{2} + \frac{2}{x})/2 ≥ 1\)
\((\frac{x}{2} + \frac{2}{x}) ≥ 2\)
C
Bunuel
General Discussion
ArunSharma12
Joined: 25 Oct 2015
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18 Mar 2020, 02:39
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[quote="Bunuel"]If x is positive, what is the least possible value of \(\frac{x}{2} + \frac{2}{x}\)?
(A) 1/2
(B) 1
(C) 2
(D) 3
(E) 4[\quote]
it'll increase for lower values of x
for x = 1; \(\frac{x}{2} + \frac{2}{x}\) = 2.5
for x = 2; \(\frac{x}{2} + \frac{2}{x}\) = 2
for x = 3; \(\frac{x}{2} + \frac{2}{x}\) = 2.16
for x = 4; \(\frac{x}{2} + \frac{2}{x}\) = 2.5
and it'll increase further for higher values of x
Ans: 2
(A) 1/2
(B) 1
(C) 2
(D) 3
(E) 4[\quote]
it'll increase for lower values of x
for x = 1; \(\frac{x}{2} + \frac{2}{x}\) = 2.5
for x = 2; \(\frac{x}{2} + \frac{2}{x}\) = 2
for x = 3; \(\frac{x}{2} + \frac{2}{x}\) = 2.16
for x = 4; \(\frac{x}{2} + \frac{2}{x}\) = 2.5
and it'll increase further for higher values of x
Ans: 2
