Home
Class 12
MATHS
Let A B C be a triangle such that /A C B...

Let `A B C` be a triangle such that `/_A C B=pi/6` and let `a , ba n dc` denote the lengths of the side opposite to `A , B ,a n dC` respectively. The value(s) of `x` for which `a=x^2+x+1,b=x^2-1,a n dc=2x+1` is(are) `-(2+sqrt(3))` (b) `1+sqrt(3)` `2+sqrt(3)` (d) `4sqrt(3)`

A

`-(2+sqrt3)`

B

`1+sqrt3`

C

`2+sqrt3`

D

`4sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|21 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|52 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

Similar Questions

Explore conceptually related problems

Let ABC be a triangle such that angleACB=pi/6 and let a , b and c denote the lengths of the side opposite to A ,B and C respectively. The value of x for which a=x^(2)+x+1,b=x^(2)-1 and c=2x+1 is

Let ABC be a triangle such that /_ACB=(pi)/(6) and let a,b and c denote the lengths of the side opposite to A,B, and C respectively.The value(s) of x for which a=x^(2)+x+1,b=x^(2)-1, and c=2x+1 is(are) -(2+sqrt(3))( b) 1+sqrt(3)2+sqrt(3)(d)4sqrt(3)

Let ABC be a triangle such that /_ABC=(pi)/(6) and let a,b and c denote the lengths of the sides opposite to A,B and C respectively. The value(s) of x for which a=x^(2)+x+1,b=x^(2)-1 and c=2x+1 is /are(a)-(2+sqrt(3))(b)1+sqrt(3)(c)2+sqrt(3) (d) 4qsrt3

If the angle A,B and C of a triangle are in an arithmetic propression and if a,b and c denote the lengths of the sides opposite to A,B and C respectively,then the value of the expression (a)/(c)sin2C+(c)/(a)sin2A is (1)/(2)(b)(sqrt(3))/(2) (c) 1(d) sqrt(3)

In a "Delta"A B C , let a ,b , and c denote the length of sides opposite to vertices A, B, and C respectively. If b=2,c=sqrt(3) and /_B A C=pi/6, then value of circumradius of triangle ABC is- 1/2 (2) 1 (3) 2 (4) 1/4

If tan^(-1)x+2cot^(-1)x=(2 pi)/(3), then x, is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3)(d)sqrt(2)

The length of the chord of the parabola y^(2)=x which is bisected at the point (2,1) is (a) 2sqrt(3)( b) 4sqrt(3)(c)3sqrt(2) (d) 2sqrt(5)

If x=5+2sqrt(6), then (x-1)/(sqrt(x)) is equal to a.sqrt(2) b.sqrt(3)c.2sqrt(2)d.2sqrt(3)

If cos^-1( (x^2-1)/(x^2+1))+ tan^-1( (2x)/(x^2-1)) = (2pi)/3 , then x equal to (A) sqrt(3) (B) 2+sqrt(3) (C) 2-sqrt(3) (D) -sqrt(3)

ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. In a triangle the sum of two sides is x and the product of the same is...

    Text Solution

    |

  2. Consider a triangle A B C and let a , ba n dc denote the lengths of th...

    Text Solution

    |

  3. In a triangle PQR, P is the largest angle and cosP=1/3. Further the in...

    Text Solution

    |

  4. Let PQR be a triangle of area Delta with a = 2, b = 7/2 and c =5/2, wh...

    Text Solution

    |

  5. If the angle A ,Ba n dC of a triangle are in an arithmetic propression...

    Text Solution

    |

  6. Let A B C be a triangle such that /A C B=pi/6 and let a , ba n dc deno...

    Text Solution

    |

  7. a triangle A B C with fixed base B C , the vertex A moves such that co...

    Text Solution

    |

  8. Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...

    Text Solution

    |

  9. A straight line through the vertex P of a triangle PQR intersects the ...

    Text Solution

    |

  10. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  11. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  12. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  13. Internal bisector of /A of triangle ABC meets side BC at D. A line dra...

    Text Solution

    |

  14. Given an isosceles triangle, whose one angle is-2pi/3 and the radius o...

    Text Solution

    |

  15. In Delta ABC, which one is true among the following ?

    Text Solution

    |

  16. Let a vertical tower A b have its end A on the level ground. Let C be ...

    Text Solution

    |

  17. ABCD is a trapezium such that AB and CD are parallel and BC | CD. If ...

    Text Solution

    |

  18. For a regular polygon, let r and R be the radii of the inscribed and ...

    Text Solution

    |

  19. In triangle A B C , let /c=pi/2dot If r is the inradius and R is circu...

    Text Solution

    |

  20. If in a DeltaABC, the altitudes from the vertices A, B, C on opposite ...

    Text Solution

    |