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If a,bgt0,aneb,and ngt1,where n is an in...

If `a,bgt0`,`aneb`,and `ngt1`,where n is an integer,then prove that `a^n+b^ngta^(n-1)b+ab^(n-1)`.

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KALYANI PUBLICATION-INEQUALITIES AND INEQUATIONS-EXERCISE
  1. If a,bgt0,aneb,and ngt1,where n is an integer,then prove that a^n+b^ng...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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