Home
Class 11
MATHS
If a ,b ,c are in G.P., prove that: a(b...

If `a ,b ,c` are in G.P., prove that: `a(b^2+c^2)=c(a^2+b^2)` `A^2b^2c^2(1/(a^3)+1/(b^3)+1/(c^3))=a^3+b^3+c^3` `((a+b+c)^2)/(a^2+b^2+c^2)=(a+b+c)/(a-b+c)` `1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)` (a+2b=2c)(a-2b+2c)`=a^2+4c^2dot`

Text Solution

Verified by Experts

N/a
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN|Exercise Exercise 9K|6 Videos

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN|Exercise Exercise 9L|10 Videos

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN|Exercise Exercise 9I|8 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN|Exercise MISCELLANEOUS EXERCISE|12 Videos

  • SETS

    NAGEEN PRAKASHAN|Exercise MISC Exercise|16 Videos

Similar Questions

Explore conceptually related problems

If a,b,c are in G.P.,prove that: a(b^(2)+c^(2))=c(a^(2)+b^(2))A^(2)b^(2)c^(2)((1)/(a^(3))+(1)/(b^(3))+(1)/(c^(3)))=a^(3)+b^(3)+c^(3)((a+b+c)^(2))/(a^(2)+b^(2)+c^(2))=(a+b+c)/(a-b+c)(1)/(a^(2)-b^(2))+(1)/(b^(2))=(1)/(b^(2)-c^(2))(a+2b=2c)(a-2b+2c)=a^(2)+4c^(2)

Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

If a + b + c = 0 , prove that a^(4) + b^(4) + c^(4) = 2(b^(2)c^(2)+c^(2)a^(2)+a^(2)b^(2)) = 1//2 (a^(2) + b^(2) + c^(2))^(2)

Prove that 2b^(2)c^(2) +2c^(2)a^(2) +2a^(2)b^(2) -a^(4)-b^(4)-c^(4)= (a+b+c) (b+c-a) (c+a-b) (a+b-c)

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

If a,b,c,d are in G.P.,prove that (a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P.and (1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P

Show that |(1,1,1), (a,b,c),(a^2,b^2,c^2)|=(a-b)(b-c)(c-a)

Prove that |{:(" "3,a+b+c,a^2+b^2+c^2),(a+b+c,a^2+b^2+c^2,a^3+b^3+c^3),(a^2+b^2+c^2,a^3+b^3+c^3,a^4+b^4+c^4):}|=|{:(1,1,1),(a,b,c),(a^2,b^2,c^2):}|^2