Home
Class 12
MATHS
Solve : |(x-2, 2x-3, 3x-4), (x-4, 2x-9, ...

Solve : `|(x-2, 2x-3, 3x-4), (x-4, 2x-9, 3x-16) ,(x-8 ,2x-27,3x-64)|=0`

Text Solution

AI Generated Solution

To solve the given determinant equation, we need to find the value of \( x \) such that: \[ \begin{vmatrix} x-2 & 2x-3 & 3x-4 \\ x-4 & 2x-9 & 3x-16 \\ x-8 & 2x-27 & 3x-64 \end{vmatrix} = 0 ...
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

Using properties of determinants, solve the following for x: |[x-2, 2x-3, 3x-4],[x-4, 2x-9, 3x-16],[ x-8, 2x-27, 3x-64]|=0

(i) Solve the equation |{:(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,2x-64):}|=0 (ii) Prove that x = 1 is a root of the equation (ii) Prove that x=1 is a root of the following equation |{:(x+1,3,5),(2,x+2,5),(2,3,x+4):}|=0 Also find the remaining roots. (iii) If a+b+c=0 then solve |{:(a-x,c,b),(c,b-x,a),(v,a,c-x):}|=0 (iv) Solve |{:(6-x,3,3),(3,4-x,5),(3,5,4-5):}|=0

Solve for xdet[[x-2,2x-3,3xx-4x-4,2x-9,3x-16x-8,2x-27,3x-64]]=0

Solve: the [[x-2.2x-3.3x-4x-4.2x-9.3x-16x-8.2x-27.3x-64]] = 0

Solve: x-(2x-(3x-4)/7)=(4x-27)/3-3 .

Solve for x: (x-2)/4+2x=3x+10

x-(2x-(3x-4)/(7))=(4x-27)/(3)-3

Solve for x: (8x-1)/2+3x-4=(1+2x)/3

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. 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

    |

  2. If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-...

    Text Solution

    |

  3. Solve : |(x-2, 2x-3, 3x-4), (x-4, 2x-9, 3x-16) ,(x-8 ,2x-27,3x-64)|=0

    Text Solution

    |

  4. If x+y+z=0 , prove that |[xa, yb,zc],[yc, za, xb], [zb, xc, ya]|=x y ...

    Text Solution

    |

  5. If a , b , c are all positive and are p t h ,q t ha n dr t h terms of ...

    Text Solution

    |

  6. Prove that: |[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-...

    Text Solution

    |

  7. |[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-a^2,ca-b^2]|...

    Text Solution

    |

  8. Prove that : |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|...

    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 that: |[a, b, ax+by],[ b, c, bx+cy], [ax+by, bx+cy,0]|=(b^2-a c)...

    Text Solution

    |

  11. Without expanding the determinant, show that (a+b+c) is a factor of th...

    Text Solution

    |

  12. If m in N and mgeq2, prove that: |1 1 1m(C1)m+1(C1)m+2(C1)m(C2)m+1(C2...

    Text Solution

    |

  13. Evaluate: =|10 ! 11 ! 12 ! 11 ! 12 ! 13 ! 12 ! 13 ! 14 !|

    Text Solution

    |

  14. Show that: |b+cc+a a+b q+r r+p p+q y+z z+xx+y|=2|a b c p q r x y z|

    Text Solution

    |

  15. Prove that |(1+a,1, 1),( 1,a+b,1),( 1, 1, 1+c)|=a b c(a+1/a+1/b+1/c)=a...

    Text Solution

    |

  16. If a , b , c , are roots of the equation x^3+p x+q=0, prove that |[a...

    Text Solution

    |

  17. If a+b+c!=0 and |(a, b, c),(b, c, a),(c,a,b)|=0 , then prove that a=b=...

    Text Solution

    |

  18. Let a , band c detnote the sides BC,CA andAB respectively of triangl...

    Text Solution

    |

  19. Prove that |[a^2+2a,2a+1,1],[2a+1,a+2,1],[3,3,1]|=(a-1)^3

    Text Solution

    |

  20. Using properties of determinant show that: |[1 , a , -bc] , [1 , b , -...

    Text Solution

    |