Home
Class 12
MATHS
Prove: |(x+4,x,x),(x,x+4,x),(x,x,x+4)|=1...

Prove: `|(x+4,x,x),(x,x+4,x),(x,x,x+4)|=16(3x+4)`

Text Solution

AI Generated Solution

To prove that \[ \left| \begin{array}{ccc} x+4 & x & x \\ x & x+4 & x \\ x & x & x+4 \end{array} \right| = 16(3x + 4), ...
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

  • DIFFERENTIABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|136 Videos

Similar Questions

Explore conceptually related problems

evaluate: |(x+4,x,x),(x,x+4,x),(x,x,x+4)|

Using properties of determinants. Find the value of 'x' |(4-x,4+x,4+x),(4+x,4-x,4+x),(4-x,4+x,4+x)|=0

Prove that : |{:(x+a,x+2a,x+3a),(x+2a,x+3a,x+4a),(x+4a,x+5a,x+6a):}|=0

The value of x for which |{:(x,2,2),(3,x,2),(3,3,x):}|+|{:(1-x,2,4),(2,4-x,8),(4,8,16-x):}|gt33 is

5(x-3)=4(3x-16)

If |[4-x, 4+x, 4+x], [4+x, 4-x, 4+x],[4+x, 4+x, 4-x]| = 0 find the value of x.

(4x+5)/(4x) = (4x)/(4x) + 5/(4x) = 1+5/(4x)

(x^(4)-16)-:(x+2)

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. Prove: |(1,a, b c),(1,b ,c a),(1,c ,a b)|=|(1,a ,a^2),( 1,b,b^2),( 1,c...

    Text Solution

    |

  2. Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b...

    Text Solution

    |

  3. Prove: |(x+4,x,x),(x,x+4,x),(x,x,x+4)|=16(3x+4)

    Text Solution

    |

  4. Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|=

    Text Solution

    |

  5. Prove: |(a, b-c,c-b),( a-c, b, c-a),( a-b,b-a, c)|=(a+b-c)(b+c-a)(c+a-...

    Text Solution

    |

  6. Prove: |a^2+1a b a c a bb^2+1b cc a c b c^2+1|=1+a^2+b^2+c^2

    Text Solution

    |

  7. Prove: |1a a^2a^2 1a a a^2 1|=(a^3-1)^2

    Text Solution

    |

  8. Prove: |b+c a a b c+a b cc a+b|=4a b c

    Text Solution

    |

  9. Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2

    Text Solution

    |

  10. Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

    Text Solution

    |

  11. Prove: |((a^2+b^2)/c,c,c),( a,(b^2+c^2)/a ,a),( b,b,(c^2+a^2)/b)|=4a b...

    Text Solution

    |

  12. Prove: |(-bc, b^2+b c,c^2+bc), (a^2+a c,-a c,c^2+a c),( a^2+a b,b^2+a ...

    Text Solution

    |

  13. |[x+lambda, 2x, 2x], [2x, x+lambda, 2x], [2x, 2x, x+lambda]| =(5x+ lam...

    Text Solution

    |

  14. सारणिकों के गुणधर्मो का प्रयोग करके प्रश्न 6 से 14 तक को सिद्ध कीजिए: ...

    Text Solution

    |

  15. Prove: |(y+z, z, y),( z, z+x,x),( y, x,x+y)|=4\ x y z

    Text Solution

    |

  16. Show that | (-a(b^2 + c^2 - a^2), 2b^3, 2c^3), (2a^3, -b(c^2 + a...

    Text Solution

    |

  17. Prove: |(1+a,1, 1),( 1, 1+a, 1),(1, 1, 1+a)|=a^3+3a^2

    Text Solution

    |

  18. Prove: |(2y, y-z-x,2y),(2z,2z, z-x-y),( x-y-z,2x,2x)|=(x+y+z)^3

    Text Solution

    |

  19. |[y+z ,x, y],[ z+y, z, x],[x+y, y ,z]|=(x+y+z)(x-z)^2

    Text Solution

    |

  20. Using properties of determinants, prove that |(a+x, y, z),( x, a+y, z...

    Text Solution

    |