Home
Class 12
MATHS
Find the value of (sqrt(2)+1)^6-(sqrt(2)...

Find the value of `(sqrt(2)+1)^6-(sqrt(2)-1)^6dot`

Text Solution

Verified by Experts

The correct Answer is:
`140sqrt(2)`
`(x+a)^(n)-(x-a)^(n) = 2[.^(n)C_(1)x^(n-1)a+.^(n)C_(3)x^(n-3)a^(3)+.^(n)C_(5)x^(n-5)a^(5)+"……"]`
`:. (sqrt(2)+1)^(6)-(sqrt(2)-1)^(6)`
`= 2[.^(6)C_(1)(sqrt(2))^(5)(1)^(1)+.^(6)C_(3)(sqrt(2))^(3)+.^(6)C_(5)(sqrt(2))^(1)(1)^(5)]`
`= 2[6 xx 4 sqrt(2) + 20 xx 2 sqrt(2) + 6 sqrt(2)]`
`= 2[24sqrt(2)+40sqrt(2)+6sqrt(2)] = 140sqrt(2)`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Concept Application Exercise 8.2|10 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Concept Application Exercise 8.3|7 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Example|10 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|7 Videos

Similar Questions

Explore conceptually related problems

Using binomial theorem, expand {(x+y)^5+(x-y)^5}dot and hence find the value of {(sqrt(2)+1)^5+(sqrt(2)-1)^5}dot

Find the value of ( sqrt(2) + 1)^(6) + ( sqrt(2) - 1)^(6) and show that the value of ( sqrt(2) + 1)^(6) lies between 197 and 198.

Find (x+1)^6+(x-1)^6 . Hence or otherwise evaluate (sqrt(2)+1)^6+(sqrt(2)-1)^6 .

Find (x+1)^6+(x-1)^6 . Hence evaluate (sqrt(2)+1)^6+(sqrt(2)-1)^6 .

Using binomial theorem, write the value of (a+b)^(6) + (a-b)^(6) and hence find the value of ( sqrt(3) + sqrt(2) )^(6) + ( sqrt(3) - sqrt(2) )^(6) .

If sqrt(2)=1.414 , then find the value of (1)/(2+sqrt(2))

If sqrt(2)=1*4 and sqrt(3)=1*7 , find the value of 1/(sqrt(3)-sqrt(2)) , correct to one place of decimal.

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

Find the value of 6/(sqrt(5)-\ sqrt(3)) , it being given that sqrt(3)=1. 732\ \ a n d\ \ sqrt(5)=2. 236

If a =( 4sqrt(6))/(sqrt(2)+sqrt(3)) then the value of (a+2sqrt(2))/(a-2sqrt(2))+(a+2sqrt(3))/(a-2sqrt(3))

CENGAGE ENGLISH-BINOMIAL THEOREM-Concept Application Exercise 8.1
  1. The first three terms in the expansion of (1+a x)^n(n!=0) are 1,6xa n ...

    Text Solution

    |

  2. If the coefficient of 4th term in the expansion of (a+b)^n is 56, then...

    Text Solution

    |

  3. The two successive terms in the expansion of (1+x)^24 whose coefficie...

    Text Solution

    |

  4. If the number of terms in the expansion of (x+y+z)^n are 36, then find...

    Text Solution

    |

  5. Find the value of 1/(81^n)-((10)/(81^n))^(2n)C1+((10^2)/(81^n))^(2n)C2...

    Text Solution

    |

  6. sum(r=0)^n(-1)^r^n Cr[1/(2^r)+3/(2^(2r))+7/(2^(3r))+(15)/(2^(4r))+ u p...

    Text Solution

    |

  7. Find n in the binomial (2^(1/3)+1/(3^(1/3)))^n , if the ration 7th ter...

    Text Solution

    |

  8. If the coefficients of (r-5)^(t h) and (2r-1)^(t h) terms in the expan...

    Text Solution

    |

  9. Find the number of irrational terms in the expansion of (5^(1//6)+2^(1...

    Text Solution

    |

  10. Represent cos 6 theta in terms of cos theta.

    Text Solution

    |

  11. Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...

    Text Solution

    |

  12. Find the value of (sqrt(2)+1)^6-(sqrt(2)-1)^6dot

    Text Solution

    |

  13. Find the degree of the polynomial 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^7-...

    Text Solution

    |

  14. Let R=(5sqrt(5)+11)^(2n+1)a n df=R-[R]w h e r e[] denotes the greatest...

    Text Solution

    |

  15. If the middle term in the binomial expansion of (1/x+xsinx)^(10) is eq...

    Text Solution

    |

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

    Text Solution

    |

  17. If the number of terms in the expansion (1+2x-3y+4z)^(n) is 286, then...

    Text Solution

    |