Prove that (a2+a3a2)>(a1+a2)(a3+a4)a1a3

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Prove that ( {a_2}{a_2 , + , a_3}) > , {a_1a_3}{(a_1 , + , a

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Prove that $(\frac{a _{2}}{a _{2} + a _{3}}) > \frac{a _{1} a _{3}}{( a _{1} + a _{2} ) ( a _{3} + a _{4} )}$

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Charlotte Discussed

Prove that

(\frac{a _{2}}{a _{2} + a _{3}}) > \frac{a _{1} a _{3}}{( a _{1} + a _{2} ) ( a _{3} + a _{4} )}

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\frac{a _{2}}{a _{2} + a _{3}} = \frac{1}{2} [\frac{a _{1}}{a _{1} + a _{2}} + \frac{a _{3}}{a _{3} + a _{4}}] =

A.M. of P and Q
which is greater than the G.M., i.e.,

PQ

Hence squaring we get the result.

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Question Text	Prove that $(\frac{a _{2}}{a _{2} + a _{3}}) > \frac{a _{1} a _{3}}{( a _{1} + a _{2} ) ( a _{3} + a _{4} )}$
Answer Type	Text solution:1
Upvotes	150