Home
Class 11
MATHS
Let a ,b ,a n dc be distinct nonzero re...

Let `a ,b ,a n dc` be distinct nonzero real numbers such that `(1-a^3)/a=(1-b^3)/b=(1-c^3)/c dot` The value of `(a^3+b^3+c^3)` is _____________.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

Let a ,b ,a n dc be distinct nonzero real numbers such that (1-a^3)/a=(1-b^3)/b=(1-c^3)/cdot The value of (a^3+b3+c^3) is _____________.

If a,b,c are positive real numbers such that a + b +c=18, find the maximum value of a^2b^3c^4

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))/((1-a)(1-b)(1-c))> 8.

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

Let a , b ,a n dc be rel numbers which satisfy the equation a+1/(b c)=1/5,b+1/(a c)=(-1)/(15),a n dc+1/(a b)=1/3dot The value of (c-b)/(c-a) is equal to ________.

Ifa, b, c are positive real number such that ab^(2)c^(3) = 64 then minimum value of ((1)/(a) + (2)/(b) + (3)/(c)) is equal to

a, b, c are reals such that a+b+c=3 and 1/(a+b) + 1/(b+c) + 1/ (c+a) = 10/3 . The value of a/(b+c) + b/(c+a) + c/(a+b) is________.

If a,b,c are distinct real numbers and |{:(a,a^(2),a^(3)-1),(b,b^(2),b^(3)-1),(c,c^(2),c^(3)-1):}|=0 then

Let a,b,c,d be real numbers such that |a-b|=2, |b-c|=3, |c-d|=4 Then the sum of all possible values of |a-d|=

If a,b,c are real numbers such that 3(a^(2)+b^(2)+c^(2)+1)=2(a+b+c+ab+bc+ca) , than a,b,c are in

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. if ax^2+bx+c = 0 has imaginary roots and a+c lt b then prove that 4a+...

    Text Solution

    |

  2. Solve: i x^2-3x-2i=0,

    Text Solution

    |

  3. Let a ,b ,a n dc be distinct nonzero real numbers such that (1-a^3)/a...

    Text Solution

    |

  4. Express each one of the following in the standard form a+i bdot (5+...

    Text Solution

    |

  5. If the cubic 2x^3-9x^2+12 x+k=0 has two equal roots then minimum valu...

    Text Solution

    |

  6. If z=4+isqrt(7) , then find the value of z^2-4z^2-9z+91.

    Text Solution

    |

  7. If the quadratic equation4x^2-2(a+c-1)x+a c-b=0(a > b > c) (a...

    Text Solution

    |

  8. If (a+b)-i(3a+2b)=5+2i , then find aa n dbdot

    Text Solution

    |

  9. If the equation x^2=a x+b=0 has distinct real roots and x^2+a|x|+b=0 h...

    Text Solution

    |

  10. Given that x, y in R. Solve: x/(1+2i)+y/(3+2i)=(5+6i)/(8i-1)

    Text Solution

    |

  11. If the equation |x^2+b x+c|=k has four real roots, then A. b^2-4cgt...

    Text Solution

    |

  12. If P(x) is a polynomial with integer coefficients such that for 4 dist...

    Text Solution

    |

  13. Let x ,y ,z ,t be real numbers x^2+y^2=9, z^2+t^2=4, and xt-y z=6 Th...

    Text Solution

    |

  14. If a ,b ,c are distinct positive numbers, then the nature of roots of...

    Text Solution

    |

  15. If (b^2-4a c)^2(1+4a^2)<64 a^2, a<0 , then maximum value of quadratic ...

    Text Solution

    |

  16. For x^2-(a+3)|x|+4=0 to have real solutions, the range of a is a. (-oo...

    Text Solution

    |

  17. The number of integral value of x satistying sqrt( x^2+10 x-16)ltx-2 ...

    Text Solution

    |

  18. If x^(2) +ax - 3x-(a+2) = 0 has real and distinct roots, then minimum ...

    Text Solution

    |

  19. Let alpha+ibeta;alpha,beta in R , be a root of the equation x^3+q x+r...

    Text Solution

    |

  20. In equation x^4-2x^3+4x^2+6x-21=0 if two its roots are equal in magn...

    Text Solution

    |