Home
Class 12
MATHS
If a, b and c are real numbers, and Delt...

If a, b and c are real numbers, and `Delta=|b+cc+a a+b c+a a+bb+c a+bb+cc+a|=0` .Show that either `a" "+" "b" "+" "c" "=" "0" "or" "a" "=" "b" "=" "c` .

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    NCERT GUJARATI|Exercise EXERCISE 4.6|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 5|23 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE|18 Videos

Similar Questions

Explore conceptually related problems

If a, b and c are real numbers , and Delta=|{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}| Show that either a+b+c=0 or a=b=c

Show that if A ⊂ B , then C – B ⊂ C – A .

Let a ,ba n dc be real numbers such that a+2b+c=4 . Find the maximum value of (a b+b c+c a)dot

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

Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C . Show that B = C .

If a, b, c are real and a!=b , then the roots ofthe equation, 2(a-b)x^2-11(a + b + c) x-3(a-b) = 0 are :

If a, b, c, d and p are different real numbers such that (a^2 + b^2 + c^2)p^2 – 2(ab + bc + cd) p + (b^2 + c^2 + d^2) le 0 , then show that a, b, c and d are in GP.

If A, B and C are angles of a triangle such that angleA is obtuse, then show tan B tan C lt 1.

If A, B and C be sets. Then, show that, A cap (B cup C) = (A cap B) cup (A cap C) .

Let A , B and C be the sets such that A uu B=A uu C and A nn B = A nn C . show that B=C

NCERT GUJARATI-DETERMINANTS -Miscellaneous Exercises on Chapter 4
  1. Prove that the determinant Delta =|{:(x,,sin0,,cos 0),(-sin 0,,-x,...

    Text Solution

    |

  2. Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( ...

    Text Solution

    |

  3. Evaluate |cosalphacosbetacosalphasinbeta-sinalpha-sinbetacosbeta0sinal...

    Text Solution

    |

  4. If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+...

    Text Solution

    |

  5. Solve the equation |x+a xxxx+a xxxx+a|=0, a!= 0

    Text Solution

    |

  6. Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...

    Text Solution

    |

  7. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

    Text Solution

    |

  8. Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]|

    Text Solution

    |

  9. Evaluate the following: |[1,x,y],[1, x+y, y],[1, x, x+y]|

    Text Solution

    |

  10. Using peoperties of determinants in questions 11 to 15, prove that : ...

    Text Solution

    |

  11. Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...

    Text Solution

    |

  12. Show that: |(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c)|=3(a+b+c)(a b...

    Text Solution

    |

  13. Show that |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p 106 p+3q|=1.

    Text Solution

    |

  14. Without expanding, show that the value of each of the determinants is ...

    Text Solution

    |

  15. Solve the system of equations2/x+3/y+(10)/z=44/x-6/y+5/z=16/x+9/y-(20)...

    Text Solution

    |

  16. Choose the correct answer in questions 17 to 19: If a, b, c are in ...

    Text Solution

    |

  17. Choose the correct answer in questions 17 to 19: If x, y, z are non...

    Text Solution

    |

  18. Let A = [(1,sin theta,1),(- sin theta,1,sin theta),(-1,-sin theta,1)],...

    Text Solution

    |