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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A DAS GUPTA-Progression, Related Inequalities and Series-Exercise

If a, b, c are in AP or GP ot HP where a>0, b>0, c>0 then prove that b...
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If a >0,b >0 and c >0 prove that (1984, 2M) (a+b+c)(1/a+1/b+1/c)geq9
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If a>0,b>0,c>0 prove that a/(b+c)+b/(c+a)+c/(a+b)ge3/2.
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If a,b,c are unequal and positive then show that (bc)/(b+c)+(ca)/(c+a)...
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If x>0, y>0, z>0, prove that x^(logy-logz)+y^(logz-logx)+z^(logx-logy)...
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If s=a+b+c+d where a, b, c, d are positive unequal numbers then prove ...
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If a, b, c are natural numbers, prove that ((a^2+b^2+c^2)/(a+b+c))^(a+...
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Prove that 1^1*2^2*3^3....n^nle((2n+1)/3)^((n(n+1))/2).
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Prove that ((n + 1)/(2))^(n) gt n!
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Prove that the product of the first n odd natural numbers cannot excee...
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If s be the sum of n positive unequal quantities a, b, c then prove th...
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If ai>0, i=1, 2, 3,..., n then prove that a1/a2+a2/a3+a3/a4+...+a(n-1)...
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If a ne b and a, b, x, y are positive rational such that x+y=1 then pr...
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If x, y, z be three sides of a triangle, prove that xyzge(y+z-x)(z+x-y...
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If a,b,c are positive real numbers and sides of a triangle, then prove...
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In a triangle ABC, prove that (1+(b-c)/a)^a*(1+(c-a)/b)^b*(1+(a-b)/c)^...
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If a+b+c=abc,a,b and c in R^(+), prove that a+b+c ge 3sqrt(3).
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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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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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If a+b+c=1 and a>0,b>0,c>0 then prove that ab^2c^3le1/(432).
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