Home
Class 11
MATHS
If x > 0, y >0, z > 0 and x +y + z = 1, ...

If `x > 0, y >0, z > 0` and `x +y + z = 1`, prove that `(1+x)(1+y)(1+z)ge 8(1-x) (1-y) (1-z)`

Promotional Banner

Topper's Solved these Questions

  • TAKI HOUSE

    UNITED BOOK HOUSE|Exercise EXERCISE|32 Videos

  • TANTIA HIGH SCHOOL

    UNITED BOOK HOUSE|Exercise EXERCISE|51 Videos

Similar Questions

Explore conceptually related problems

If y is the H.M. between x and z, prove that, (1)/(y-x) + (1)/(y-z) = (1)/(x) + (1)/(z) .

AB, CD, PQ are perpendicular to BD. If AB = x, CD = y and PQ = z prove that (1)/(x) + (1)/(y) = (1)/(z)

If x+y+z=x y z prove that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/(1-x^2)(2y)/(1-y^2)(2z)/(1-z^2)dot

If x+z = 2y " and " b^2 = ac , then prove that a^(y-z)*b^(z-x)*c^(x-y) =1 .

Prove that log_(1/y)x xx log_(1/z)yxx log_(1/x)z=-1

If a^(x)=b^(y)=c^(z) and b^(2)=ac prove that (1)/(x)+(1)/(z)=(2)/(y)

If x + y + z = xyz and x, y, z gt 0 , then find the value of tan^(-1) x + tan^(-1) y + tan^(-1) z

If x, y, z are integers such that x ge 0, y ge 1, z ge 2 and x + y + z = 15, then the number of ordered triplets of the from (x,y,z) is

If cos^-1 x +cos^-1y + cos^-1z = pi and x + y + z = 3/2 , then show that x = y = z.

If z=x+iy and |2z-1| =|z-2|then prove that x^2+y^2=1

UNITED BOOK HOUSE-Taki House Govt. Sponsored Girls High School, Question Paper -Exercise
  1. The mode can be obtained geometrically from

    Text Solution

    |

  2. Bar diagrams are applicable to represent.

    Text Solution

    |

  3. What is the difference between line diagram and ratio chart?

    Text Solution

    |

  4. Define frequency density of a class interval.

    Text Solution

    |

  5. The A.M. of 1, 2, 2^2,……..2^9 is(fill in the blanks)

    Text Solution

    |

  6. The difference between the upper and lower limits of a class interval ...

    Text Solution

    |

  7. Describe cross sectional data with their utility.

    Text Solution

    |

  8. Define ordianl and nominal data.

    Text Solution

    |

  9. If the relation between two variables y and x is x - 3y = 6 and S.D. o...

    Text Solution

    |

  10. What are the merits of arithmetic mean?

    Text Solution

    |

  11. Write the two meanings of statistics.

    Text Solution

    |

  12. Write down the merits and demerits of mass questionnaire method.

    Text Solution

    |

  13. Write the significance of E.T.S.

    Text Solution

    |

  14. Compare bantulation with diagrammatic representation of data.

    Text Solution

    |

  15. How would you construct a frequency distribution of a continuous varia...

    Text Solution

    |

  16. If x > 0, y >0, z > 0 and x +y + z = 1, prove that (1+x)(1+y)(1+z)ge 8...

    Text Solution

    |

  17. Find the arithmetic mean of 7, 77, 777.upto p^(th) term.

    Text Solution

    |

  18. If the values of a variable are in G.P, then prove that A.M., G.M., H....

    Text Solution

    |

  19. For a set of positive quantities, Prove that A.M. ge GM ge H.M..

    Text Solution

    |

  20. Show that overset(n)underset(i=1)sum (xi - A)^2 is minimum when A = ba...

    Text Solution

    |