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Prove that (a^2+b^2)/2gt((a+b)/2)(aneb...

Prove that
`(a^2+b^2)/2gt((a+b)/2)(aneb)`.

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KALYANI PUBLICATION-INEQUALITIES AND INEQUATIONS-EXERCISE
  1. Prove the following where a,b,x m,ngt0 (a^3+b^3)/(a^2+b^2)gt(a^2+b^2...

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  2. Prove that 1/(a+b)+1/(a-b)gt1/sqrt(a^2-b^2)(agtb).

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  3. Prove that (a^2+b^2)/2gt((a+b)/2)(aneb).

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  4. Prove that (a+b)^2gt14(a+b)-49(agt0,bgt0).

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  5. Find the value of x for which the following expressions aquire greates...

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  6. Find the value of x for which the following expressions acquire greate...

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  7. Find the value of x for which the following expression...

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  8. Find the value of x for which the following expression...

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  9. Find the greatest value of x in order that. 7x^2+11gex^3+17x.

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  10. Find the least value of x in order that. 3x^3+7xge8x^2+2.

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  11. (b^3+c^3)/(b+c)+(c^3+a^3)/(c+a)+(a^3+b^3)/(a+b)gtab+bc+ca

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  12. If a,b,c are positive unequal real numbers then prove that 1/a+1/b+1...

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  13. If a,b,c are positive unequal real numbers then prove that (bc)/a+(c...

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  14. If a,b,c are positive unequal real numbers then prove that b^2c^2+c^...

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  15. If a,b,c are positive unequal real numbers then prove that (a+b+c)(1...

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  16. If a,b,c,e,f,g are positive unequal real numbers then prove that (a/...

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  17. If a,b,c are positive unequal real numbers then prove that a^2+b^2+c...

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  18. prove that sqrt7+sqrt12gtsqrt6+sqrt13.

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  19. If a,b,c are positive unequal real numbers then prove that sqrt14+sq...

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  20. Prove that in any triangle, the semi perimeter is greater than each of...

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