Finding least value.
Algebra
Level
3
Find the least possible value of (a/b + b/c + c/d + d/a) . Where , a,b,c,d are real positive numbers.
The answer is 4.00.
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1 solution
As, a,b,c,d are real positive numbers, then (a/b), (b/c) , (c/d) , (d/a) are also real positive numbers. Now, A.M >= G.M Hence, {( a/b + b/c + c/d + d/a )/ 4} >= ( a/b* b/c * c/d * d/a)^1/4 =1 Implies that, (a/b + b/c +c/d + d/a) >= 1*4 = 4