If a,b,c,d are four positive numbers then

JEE Advanced Mathematics question

If are four positive numbers then

(A)\left(\dfrac ab+\dfrac bc\right)\left(\dfrac cd+\dfrac de\right)\ge4\cdot\sqrt{\dfrac ae}Correct
(B)\left(\dfrac ab+\dfrac cd\right)\left(\dfrac bc+\dfrac de\right)\ge4\cdot\sqrt{\dfrac ae}Correct
(C)\dfrac ab+\dfrac bc+\dfrac cd+\dfrac de+\dfrac ea\ge5Correct
(D)\dfrac ba+\dfrac cb+\dfrac dc+\dfrac ed+\dfrac ae\ge\dfrac15Correct

Answer: (A),(B),(C),(D)

Solution

(The options involve a fifth number ; read the stem as " are five positive numbers".) All parts use AM GM. - (a) ✓: and . Multiplying (both sides positive): product . -

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Question ID VK-107879