Home
Class 11
MATHS
If a,b,c are different positive real num...

If a,b,c are different positive real numbers such that `b+c−a,c+a−b` and `a+b−c` are positive, then `(b+c−a)(c+a−b)(a+b−c)−abc` is a. positive b. negative c. non-positive d. non-negative

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|9 Videos
  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

If a,b,c,d are distinct positive numbers in AP, then

If a,b,c are three distinct positive real number such that a^2+b^2+c^2=1 , then ab+bc+ca=1 is

If a, b and c are three positive real numbers, show that a^2 + b^2 + c^2 ge ab + bc + ca

If a,b,c,d are positive real number such that a+b+c+d=2 , then M=(a+b)(c+d) satisfies the relation:

If a, b and c are three positive real numbers, then show that a^3 + b^3 + c^3 > 3abc .

If a ,b , a n dc are distinct positive real numbers such that a+b+c=1, then prove that (1-a)(1-b)(1-c)> 8.

Factorise : (b+c-a)(c+a-b)(a+b-c)+8abc

If a,b,c are positive real number, then the least value of (a+b+c)(1/a+1/b+1/c) is

Let a, b , c, p , q , r be positive real numbers such that a , b , c are in G.P. and a^p = b^q = c^r . Then

If a , b ,c are three distinct positive real numbers in G.P., then prove that c^2+2a b >3ac

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. Given that x ,y ,z are positive real such that x y z=32. If the minimu...

    Text Solution

    |

  2. If the product of n positive numbers is n^n , then their sum is (a)...

    Text Solution

    |

  3. If a,b,c are different positive real numbers such that b+c−a,c+a−b and...

    Text Solution

    |

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

    Text Solution

    |

  5. Find the maximum value of (7−x)^4 (2+x)^5 when x lies between −2 and ...

    Text Solution

    |

  6. If a1, a2,...... ,an >0, then prove that (a1)/(a2)+(a2)/(a3)+(a3)/(a4...

    Text Solution

    |

  7. If a > b and n is a positive integer, then prove that a^n-b^n > n(a b)...

    Text Solution

    |

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

    Text Solution

    |

  9. 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

    |

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

    Text Solution

    |

  11. Prove that 2/(b+c)+2/(c+a)+2/(a+b)lt1/a+1/b+1/c ,where a ,b ,c>0.

    Text Solution

    |

  12. The minimum value of 2^(sin x) + 2^(cos x) is

    Text Solution

    |

  13. In how many parts an integer N>=5 should be divide so that the produc...

    Text Solution

    |

  14. In triangle ABC internal angle bisector AI,BI and CI are produced to m...

    Text Solution

    |

  15. The minimum value of (x^4+y^4+z^2)/(x y z) for positive real numbers x...

    Text Solution

    |

  16. If x ,y ,z are positive real number, then show that sqrt((x^(-1)y)xsqr...

    Text Solution

    |

  17. The least value of 6tan^2varphi+54cot^2varphi+18 is (I)54 when A.M.g...

    Text Solution

    |

  18. A rod of fixed length k slides along the coordinates axes, If it meet...

    Text Solution

    |

  19. If y=3^(x-1)+3^(-x-1) , then the least value of y is (a)2 (b)6 (c...

    Text Solution

    |

  20. If a b^2c^3, a^2b^3c^4,a^3b^4c^5 are in A.P. (a ,b ,c >0), then the mi...

    Text Solution

    |