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If a>0,b>0,c>0 prove that a/(b+c)+b/(c+a...

If `a>0,b>0,c>0` prove that `a/(b+c)+b/(c+a)+c/(a+b)ge3/2`.

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ML KHANNA-INEQUALITIES-PROBLEM SET (1)(TRUE AND FALSE)
  1. If a>0,b>0,c>0 prove that a/(b+c)+b/(c+a)+c/(a+b)ge3/2.

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  2. If n is a positive integer then 2^(n)gt1+nsqrt((2^(n-1))). True or Fal...

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  3. If a,b,c are in HP, then prove that (a+b)/(2a-b)+(c+b)/(2c-b)gt4.

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  4. If a > ba n dn is a positive integer, then prove that a^n-b^n > n(a b)...

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  5. If agtbgt1 then a^(n)-b^(n)gtn(a-b) for every +ive integer n ge2.True ...

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  6. 2/(b+c)+2/(c+a)+2/(a+b)gt9/(a+b+c)

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  7. If S=a+b+c then prove that (S)/(S-a)+(S)/(S-b)+(S)/(S-c) gt (9)/(2) wh...

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  8. 3/(b+c+d)+3/(c+d+a)+3/(d+a+b)+3/(a+b+c)gt16/(a+b+c+d)

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  9. n(n+1)^(3)lt8(1^(3)+2^(3)+3^(3)+………+n^(3))

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  10. If a, b, c are in H.P. and they are distinct and positive then prove t...

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  11. Sum of the nth powers of the m^(th) power of n even numbers is gtn(n+1...

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  12. If a,b,c are real numbers such that a^(2)+b^(2)+c^(2)=1 then ab+bc+cag...

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  13. In any triangle the semi perimeter is greater than each of its sides.

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  14. The sum of the cubes of the legs of a right angled triangle is less th...

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  15. Thesum of the hypotenuse and the altitude of a right angled triangle d...

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  16. The area of an arbitrary triangle is less than one fourth the square o...

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  17. If x,y,z are all positive and x lt y lt z, then (x^(2))/zlt(x^(2)+y^(2...

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  18. If 0ltalpha(1)ltalpha(2)lt……….ltalpha(n)lt(pi)/2 then tan alpha(1)lt...

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  19. If A+B+C=pithen "tan"^(2)A/2+"tan"^(2)B/2+"tan"^(2)C/2ge1.

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  20. Prove that 2sinx + tanx ge3x, for all x in [0, pi/2].

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