ncert cbse chapter 8 binomial theorem miscellaneous exercise
5.evaluate { (sqrt(3) + sqrt(2))^6 } - { (sqrt(3) - sqrt(2))^6 }
(a+b)^6 = {a^6} + C(6,1){a^5}{b} +C(6,2){a^4}{b^2}+C(6,3){a^3}{b^3} +C(6,4){a^2}{b^4}++C(6,5){a^1}{b^5}+C(6,6)(b)^6
C(6,1) = 6 =C(6,5)
C(6,2)=15=C(6,4)
C(6,3)=20
C(6,6)=1
(a+b)^6 = {a^6} + 6{a^5}{b} +15{a^4}{b^2}+20{a^3}{b^3} +15{a^2}{b^4}+6{a^1}{b^5}+(b)^6
(a-b)^6 = {a^6} - 6{a^5}{b} +15{a^4}{b^2} - 20{a^3}{b^3} +15{a^2}{b^4}- 6{a^1}{b^5}+(b)^6
adding the two equations
{ (a+b)^6} - {(a-b)^6} =
2[6{a^5}{b} +20{a^3}{b^3}+ 6{a^1}{b^5} ]
a=sqrt(3)
b=sqrt(2)
{ (sqrt(3) + sqrt(2))^6 } - { (sqrt(3) - sqrt(2))^6 }
= 2[6*{(sqrt(3))^5}{(sqrt(2))} +20{(sqrt(3))^3}{(sqrt(2))^3}+6{(sqrt(3))^1}{(sqrt(2))^5} ]
=2[54+120+24 ] {sqrt(6)}
=396*sqrt(6)
chapter 8 binomial theorem miscellaneous exercise
1.Find a , b and n in the expansion of (a+b)^n if the first three terms in the expansion are 729, 7290, 30375
2. Find a if the coefficients of (x^2) & (x^3) in the expansion of {(3+ax)^9} are equal
3.find the coefficient of {x^5} in the expansion of{(1+2x)^6}{(1-x)^7}
5.evaluate { (sqrt(3) + sqrt(2))^6 } - { (sqrt(3) - sqrt(2))^6 }
disclaimer:
There is no guarantee about the data/information on this site. You use
the data/information at your own risk. You use the advertisements
displayed on this page at your own risk.We are not responsible for the
content of external internet sites. Some of the links may not work.
Your internet usage may be tracked by the advertising networks using
tracking cookies
No comments:
Post a Comment
please leave your comments