Home
Class 9
MATHS
If a b c=1,\ show that 1/(1+a+b^(-1))+1...

If `a b c=1,\ ` show that `1/(1+a+b^(-1))+1/(1+b+c^(-1))+1/(1+c+a^(-1))=1`

Promotional Banner

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    RD SHARMA ENGLISH|Exercise All Questions|23 Videos

  • FACTORIZATION OF ALGEBRAIC EXPRESSIONS

    RD SHARMA ENGLISH|Exercise All Questions|226 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are in G.P. show that (1)/(a^(2)),(1)/(b^(2)),(1)/(c^(2)) are also in G.P.

Show that |1a b_c1b c+a1c a+b|=0

If b is the harmonic mean between a and c, then prove that (1)/(b - a) + (1)/(b - c) = (1)/(a) + (1)/(c)

If a,b,c are in A.P. show that a((1)/(b)+(1)/(c)),b((1)/(c)+(1)/(a)), c((1)/(a)+(1)/(b)) are in A.P.

Prove that: (a+b+c)/(a^(-1)\ b^(-1)+b^(-1)\ c^(-1)+c^(-1)a^(-1))=a b c

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

Show that: 1/(1+x^(b-a)+x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-c)+\ x^(a-c))=1

Using properties of determinants, show that |1 a a^2 -b c 1 b b^2 -c a 1 c c^2 -a b|=0

If a > b > c >0 , prove that cot^(-1)((a b+1)/(a-b))+cot^(-1)((b c+1)/(b-c))+cot^(-1)((c a+1)/(c-a))=pi

Show that a^(2)(1+b^(2))+b^(2)(1+c^(2))+c^(2)(1+a^(2))gt abc

RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. Prove that: (a+b+c)/(a^(-1)\ b^(-1)+b^(-1)\ c^(-1)+c^(-1)a^(-1))=a b c

    Text Solution

    |

  2. Prove that: (a^(-1)+b^(-1))^(-1)=(a b)/(a+b)

    Text Solution

    |

  3. If a b c=1,\ show that 1/(1+a+b^(-1))+1/(1+b+c^(-1))+1/(1+c+a^(-1))=1

    Text Solution

    |

  4. Simplify the following: (i)\ (3^n\ xx\ 9^(n+1))/(3^(n-1)\ xx\ 9^(n-1))...

    Text Solution

    |

  5. Simplify the following: (i)\ (5^(n+3)-\ 6\ xx\ 5^(n+1))/(9\ xx\ 5^n-2^...

    Text Solution

    |

  6. Solve the following equations for x\ : (i)\ 7^(2x+3)=1 (ii)\ 2^(x+1)...

    Text Solution

    |

  7. Solve the following equations for x\ : (i)\ 4^(2x)=1/(32) (ii)\ 4^...

    Text Solution

    |

  8. Solve the following equations for x\ : (i)\ 2^(2x)-\ 2^(x+3)+2^4=0 ...

    Text Solution

    |

  9. If 49392=a^4b^2c^3, find the value of a ,\ b\ a n d\ c , where a ,\ b\...

    Text Solution

    |

  10. If 1176=2^a xx\ 3^b xx\ 7^c , and a , b\ a n d\ c are natural numbers...

    Text Solution

    |

  11. Given 4725=3^a5^b7^c , find the integral values of a ,\ b\ a n d\ c t...

    Text Solution

    |

  12. If a=x y^(p-1),\ b=x y^(q-1) and c=x y^(r-1) , prove that a^(q-r)b^(r-...

    Text Solution

    |

  13. Find the value of: (8/(27))^(1/3)

    Text Solution

    |

  14. Find the value of : ((32)/(243))^(1/5)

    Text Solution

    |

  15. Find the value of: (1/(64))^(1/6)

    Text Solution

    |

  16. Evaluate each of the following by removing radical signs and negative ...

    Text Solution

    |

  17. Evaluate each of the following by removing radical signs and negative ...

    Text Solution

    |

  18. Simplify each of the following: (i)\ (625)^(-1/4) (ii)\ ((256)/(81)...

    Text Solution

    |

  19. Simplify each of the following: (i)\ ((243)/(32))^(-4/5) (ii)\ (32...

    Text Solution

    |

  20. [{(625)^(-1/4)}^(-1/2)]^2

    Text Solution

    |