Home
Class 12
MATHS
If y z+z x+x y=12 ,w h e r ex ,y ,z are ...

If `y z+z x+x y=12 ,w h e r ex ,y ,z` are positive values, find the greatest value of `x y zdot`

Text Solution

Verified by Experts

Using A.M `ge` G.M we have
`(xy + yz + zx)/(3) ge (x^(2) y^(2) z^(2))^(1//3)`
`implies (x)/(3) ge (x^(2) y^(2) z^(2))^(1//2)`
`implies (xyz)_("max") = ((12)/(3))^(3//2)`
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Example 1|1 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Example 2|1 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Comprehension|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

  • INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|762 Videos

Similar Questions

Explore conceptually related problems

If y z+z x+x y=12 , and x , y , z are positive values, find the greatest value of x y zdot

If x=c y+b z ,y=a z+c x ,z=bx+a y ,w h e r e .x ,y ,z are not all zeros, then find the value of a^2+b^2+c^2+2a b c dot

If x, y, z are the three consecutive term of an AP, then the value of x + y + z is

Given a=x//(y-z), b=y//(z-x), and c=z//(x-y),w h e r e .x , y and z are not all zero, then the value of a b+b c+c a is a. 0 b. 1 c. -1"" d. none of these

If 5, x, y, z, 405, are the first five terms of a G.P., find the values of x, y, z.

If x ,y and z are positive real umbers and x=(12-yz)/(y+z) . The maximum value of x y z equals.

If x,y,z be three positive numbers such that xyz^(2) has the greatest value (1)/(64) , then the value of (1)/(x)+(1)/(y)+(1)/(z) is

Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonzero real number, is equal to a. x y z b. 2x y z c. 3x y z d. 4x y z

The value of |[yz, z x,x y],[ p,2p,3r],[1, 1, 1]|,w h e r ex ,y ,z are respectively, pth, (2q) th, and (3r) th terms of an H.P. is a. -1 b. 0 c. 1 d. none of these

Find the greatest value of x^2y^3z^4 if x+y+z=1,w h e r ex ,y ,z are positive.

CENGAGE PUBLICATION-INEQUALITIES INVOLVING MEANS -Illustration
  1. about to only mathematics

    Text Solution

    |

  2. If a+b+c=1, then prove that 8/(27a b c)>{1/a-1}{1/b-1}{1/c-1}> 8.

    Text Solution

    |

  3. If y z+z x+x y=12 ,w h e r ex ,y ,z are positive values, find the grea...

    Text Solution

    |

  4. If a ,b ,c are positive, then prove that a//(b+c)+b//(c+a)+c//(a+b)geq...

    Text Solution

    |

  5. Prove that 2^n >1+nsqrt(2^(n-1)),AAn >2 where n is a positive integer.

    Text Solution

    |

  6. If S+a1+a2+a3++an ,a1 in R^+ for i=1ton , then prove that S/(S-a1)+S/...

    Text Solution

    |

  7. If a1+a2+a3+......+an=1 AA ai > 0, i=1,2,3,......,n, then find the ma...

    Text Solution

    |

  8. If a , b , c , are positive real numbers, then prove that (2004, 4M) {...

    Text Solution

    |

  9. Prove that (sec^4alpha)/(tan^2beta)+(sec^4beta)/(tan^2alpha)ge8. If ea...

    Text Solution

    |

  10. Prove that [(x^2+y^2+z^2)/(x+y+z)]^(x+y+z)> x^x y^y z^z >[(x+y+z)/3]^(...

    Text Solution

    |

  11. Prove that 1^1xx2^2xx3^3xxxxu nlt=[(2n+1)//3]n(n+1)//2,n in Ndot

    Text Solution

    |

  12. Find the greatest value of x^2 y^3, where x and y lie in the first qua...

    Text Solution

    |

  13. Find the maximum value of (7-x)^4(2+x)^5w h e nx lies between -2a n d7...

    Text Solution

    |

  14. Find the maximum value of xyz when (x)/(1)+(y^2)/(4)+(z^3)/(27)=1, whe...

    Text Solution

    |

  15. If a ,b >0 such that a^3+b^3=2, then show that a+blt=2.

    Text Solution

    |

  16. If m >1,n in N show that 1m+2m+2^(2m)+2^(3m)++2^(n m-m)> n^(i-m)(2^n-...

    Text Solution

    |

  17. Prove that in an acute angled triangle ABC , sec A+sec B +sec Cge 6.

    Text Solution

    |

  18. Prove that (b^2+c^2)/(b+c)+(c^2+a^2)/(c+a)+(a^2+b^2)/(a+b)> a+b+c

    Text Solution

    |

  19. Prove that (a^8+b^8+c^8)/(a^3b^3c^3)>1/a+1/b+1/c

    Text Solution

    |

  20. If a ,b ,a n dc are positive and a+b+c=6, show that (a+1//b)2+(b+1//c)...

    Text Solution

    |