Home
Class 12
MATHS
Evaluate the following: \ (x+sqrt(x^2-1)...

Evaluate the following: `\ (x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6`

Text Solution

Verified by Experts

The correct Answer is:
`2x^(12)+15x^(10)-29x^(6)+12x^(4)+3x^(2)-1}`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (section-A)|50 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (section-B)|34 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE ENGLISH|Exercise Illustration|1 Videos

  • APPLICATION OF INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - I Aakash Challengers Questions|2 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise section-J (Aakash Challengers Qestions)|13 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following: (sqrt(x+1)+sqrt(x-1))^6+(sqrt(x+1)-sqrt(x-1))^6

Find the number of terms in the expansion of (x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6

Evaluate the following limit: (lim)_(x->2)(sqrt(x^2+1)-sqrt(5))/(x-2)

Evaluate the following limit: (lim)_(x->1)((2x-3)(sqrt(x)-1))/(3x^2+3x-6)

Evaluate the following: lim_(xrarr2)(x^2-4)/(sqrt(3x-2)-sqrt(6-x))

Differentiate the following function (sqrt(x^2+1)+sqrt(x^2-1))/(sqrt(x^2+1)-sqrt(x^2-1)

Evaluate the following limits : Lim_( xto 1) (sqrt((x^(2)-1 ))+sqrt((x-1)))/(sqrt((x^(2)-1)))

Evaluate the following limit: (lim)_(x->1)(sqrt(5x-4)-sqrt(x))/(x^2-1)

Evaluate the following limit: (lim)_(x->0)(sqrt(1+x^2)-sqrt(1-x^2))/x

Let coefficient of x^4 and x^2 in the expansion of (x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6 is alpha and beta then alpha-beta is equal to

AAKASH INSTITUTE ENGLISH-BINOMIAL THEOREM-Try Yourself
  1. What is the last entry of any row of pascle's triangle?

    Text Solution

    |

  2. What is the 6th sicth entry in row 5 of pascle's triangle?

    Text Solution

    |

  3. Expand (i) (x/3+3y/2)^(5) ,(ii) (x^(2)+2/x)^(4) using pascle's trian...

    Text Solution

    |

  4. Expand (2x^(2) + 4y^(2))^(6) using pascals triangle.

    Text Solution

    |

  5. Expand (i) (x+1/x)^(7) , (ii) (x^(2)+2/x)^(4) using binomial theorem.

    Text Solution

    |

  6. Expand (i) ((2x)/3-(3)/(2x))^(6) , (ii) (2/x-x/2)^(5)

    Text Solution

    |

  7. Byusing binomial theorem evaluate (i) (101)^(3) , (ii) (47)^(4)

    Text Solution

    |

  8. Byusing binomial theorem evaluate (i) (107)^(5) , (ii) (55)^(3)

    Text Solution

    |

  9. Using bionomial theorem, show that (9^(n)-8n-1) is always divisible by...

    Text Solution

    |

  10. With the help of bionomial expansion, show that (4^(n)-3n) is always l...

    Text Solution

    |

  11. Find (1+x)^(4) + (1-x)^(4). Hence evaluate (sqrt2+1)^(4) + (sqrt2-1)^(...

    Text Solution

    |

  12. Find (1+x)^(6) - (1-x)^(6). Hence evaluate (1+sqrt3)^(6) - (1-sqrt3)^(...

    Text Solution

    |

  13. Find the fifth expansion of (a/3-3b)^(7)

    Text Solution

    |

  14. Find the fifth expansion of (2x^(2)-1/(3x^(2)))^(10)

    Text Solution

    |

  15. Write down the general term in the expansion of (x^(2)-y^(3))^6. (ii...

    Text Solution

    |

  16. Find the middle term in the expansion of (1+3x+3x^(2)+x^(3))^(2n)

    Text Solution

    |

  17. If in the expansion of (1+x)^(15), the coefficients of (r+3)^(t h)a n ...

    Text Solution

    |

  18. Evaluate the following: \ (x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6

    Text Solution

    |

  19. if (1+a)^(n)=.^(n)C(0)+.^(n)C(1)a++.^(n)C(2)a^(2)+ . . .+.^(n)C(n)a^(n...

    Text Solution

    |

  20. If (1+a)^(n)=.^(n)C(0)+.^(n)C(1)a+.^(n)C(2)a^(2)+ . . +.^(n)C(n)a^(n),...

    Text Solution

    |