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If a,b,c gt 0 show that (bc)/(b+c)+(ca)/...

If `a,b,c gt 0` show that `(bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)le(a+b+c)/2`.

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
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  2. If x and y are positive quantities whose sum is 4, show that (x+1/x)^2...

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  3. If a,b,c gt 0 show that (bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)le(a+b+c)/2.

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  4. Show that a^2(1+b^2)+b^2(1+c^2)+c^2(1+a^2)ge6abc.

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  6. Prove that ((bc+ac+ab)/(a+b+c))^(a+b+c)ge(b)^a(c)^b(a)^c [where a,b,c ...

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  8. If the ratiio of the sum of n terms ofd two AP's is (3n+1):(2n+3) then...

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  10. Given p no. of A.P. each of which consists of an n terms. If their fir...

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  11. Answer the following question based on above passage: The coefficient...

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  12. If a,b,c ,d and p are distinct real number such that (a^2+b^2+c^2)p^2-...

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  13. Suppose a,b,c are in A.P and a^2,b^2,c^2 are in G.P. If a lt b lt c an...

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  14. The value of 4^(1/3).4^(1/9).4^(1/27)....infty is.

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  15. If the sum of an infinite GP is 20 and sum of their square is 100 then...

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  16. If S=1+a+a^2+....... t o infty , then a=

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  17. If 4a^2+9b^2+16c^2=2(3ab+6bc+4ca) where a,b,c are non zero real number...

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  18. If a,b,c in AP and x=sum(n=0)^inftya^n,y=sum(n-0)^inftyb^n,z=sum(n-0)^...

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  19. If a,b,c are in G.P., then the equations ax^2+2bx+c =0 and dx^2+2ex+f ...

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  20. If the product of n positive number is unity, then their sum is

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