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Compare the pairs of real number given b...

Compare the pairs of real number given below
`a^3+1,a^2+1`.

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KALYANI PUBLICATION-INEQUALITIES AND INEQUATIONS-EXERCISE
  1. State whether the following statements are true or false. If false giv...

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  2. State whether the following statements are true or false. If false giv...

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  3. Compare the pairs of real number given below a^3+1,a^2+1.

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  4. Compare the pairs of real number given below a^3+b^3,a^2b+ab^2.

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  5. Compare the pairs of real number given below ab+1,a+b.

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  6. Prove the following where a,b,x m,ngt0 m^5+n^5gem^4n-mn^4.

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  7. Prove the following where a,b,x m,ngt0 a^6+b^6gea^5b+ab^5.

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  8. Prove the following where a,b,x m,ngt0 a^(m+n)+b^(m+n)gea^mb^n+a^nb^...

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  9. Prove the following where m,ngt0 m^3-n^3gt(m-n)^3, (mgtn).

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  10. Prove the following where a,b,m,ngt0 (m+2n)/(m+3n)ge(m+n)/(m+2n).

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  11. Prove the following where a,b,x m,ngt0 (m^3+n^3)/(m^2+n^2)ge(m^2+n^2...

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  12. Prove the following where a,b,x m,ngt0 (a-c)/bge(b-c)/a+(a-b)/b(0lta...

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

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

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

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

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

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

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

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