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If x, y, z are all positive real number...

If x, y, z are all positive real numbers, then prove that,
If `x+y+z=1`, then prove that `(1-x)(1-y)(1-z)ge8xyz`.

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KALYANI PUBLICATION-INEQUALITIES AND INEQUATIONS-EXERCISE
  1. If a,b, c and x, y, z are all positive and unequal, then prove that, ...

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  2. If a,b, c and x, y, z are all positive and unequal, then prove that, ...

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  3. If x, y, z are all positive real numbers, then prove that, If x+y+z...

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  4. If a,b, c and x, y, z are all positive and unequal, then prove that, ...

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  5. If x + y=5, then find the greatest value of 10xy.

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  6. If 2x+ 3y = 5, then find the greatest value of 8xy.

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  7. If 7/12xy=21, then find the minimum value of 5(x+y).

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  8. Find the solution sets of the following inequations. 7(3-2x)+5(x-1)l...

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  9. Find the solution sets of the following inequations. 5(x-11)+4gt2(x-...

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  10. Find the solution sets of the following inequations. 8(2x-7)-9(3x-14...

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  11. Find the solution sets of the following inequations. 13x-4(5x-8)+17g...

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  12. Find the solution sets of the following inequations. 14(x-4)+3(x+5)l...

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  13. Find the solution sets of the following inequations. a^2(x-a)+b^2(x-...

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  14. Find the solution sets of the following inequations. (x-6)/5+(x-4)/3...

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  15. Find the solution sets of the following inequations. x/10+(2x-13)/9g...

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  16. Find the solution sets of the following system of inequations. 4x+3g...

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  17. Find the solution sets of the following system of inequations. 5(1-x...

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  18. Find the solution sets of the following system of inequations. 3x+2l...

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  19. Find the solution sets of the following system of inequations. 4(x-3...

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  20. Find the solution sets of the following system of inequations. 3(x-2...

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