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If x>0, y>0, z>0, prove that x^(logy-log...

If `x>0, y>0, z>0`, prove that `x^(logy-logz)+y^(logz-logx)+z^(logx-logy)ge3`.

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A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
  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 a,b,c are unequal and positive then show that (bc)/(b+c)+(ca)/(c+a)...

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  3. If x>0, y>0, z>0, prove that x^(logy-logz)+y^(logz-logx)+z^(logx-logy)...

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  4. If s=a+b+c+d where a, b, c, d are positive unequal numbers then prove ...

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  5. If a, b, c are natural numbers, prove that ((a^2+b^2+c^2)/(a+b+c))^(a+...

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  6. Prove that 1^1*2^2*3^3....n^nle((2n+1)/3)^((n(n+1))/2).

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  7. Prove that ((n + 1)/(2))^(n) gt n!

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  8. Prove that the product of the first n odd natural numbers cannot excee...

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  9. If s be the sum of n positive unequal quantities a, b, c then prove th...

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  10. If ai>0, i=1, 2, 3,..., n then prove that a1/a2+a2/a3+a3/a4+...+a(n-1)...

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  11. If a ne b and a, b, x, y are positive rational such that x+y=1 then pr...

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  12. If x, y, z be three sides of a triangle, prove that xyzge(y+z-x)(z+x-y...

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  13. If a,b,c are positive real numbers and sides of a triangle, then prove...

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  14. In a triangle ABC, prove that (1+(b-c)/a)^a*(1+(c-a)/b)^b*(1+(a-b)/c)^...

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  15. If a+b+c=abc,a,b and c in R^(+), prove that a+b+c ge 3sqrt(3).

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  16. If a+2b+3c=1 and a>0 , b>0 , c>0 and the greatest value of a^3b^2c is...

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  17. If 4a+3b+2c=5 and a>0,b>0,c>0 then the greatest value of a^2b^3c^4 wil...

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  18. If a+b+c=1 and a>0,b>0,c>0 then prove that ab^2c^3le1/(432).

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  19. Find the greatest value of the product of three positive numbers if th...

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  20. Find the sum of n terms of the series 1*2*3+2*3*4+3*4*5...........

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