Home
Class 12
MATHS
Prove that (1)/(a) + (1)/(b) + (1)/(c ) ...

Prove that `(1)/(a) + (1)/(b) + (1)/(c ) ge (1)/(sqrt((bc))) + (1)/(sqrt((ca))) + (1)/(sqrt((ab)))`, where a,b,c `gt` 0

Text Solution

Verified by Experts

`(1)/(b)+(1)/(c) ge 2[(1)/(b)(1)/(c)]^(1///2)`
`(1)/(a)+(1)/(b) ge 2[(1)/(a)(1)/(b)]^(1//2)`
`(1)/(a)+(1)/(c) ge 2 [(1)/(a)(1)/(c)]^(1//2)`
Adding, we get
`(1)/(a)+(1)/(b)+(1)/(c)ge (1)/(sqrt(bc))+(1)/(sqrt(bc))+(1)/(sqrt(ab))`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Exercise 6.2|6 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Exercise 6.3|6 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Examples|37 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

  • INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|324 Videos

Similar Questions

Explore conceptually related problems

(1)/(log_(sqrt(b))abc)+(1)/(log_(sqrt(ca))abc)+(1)/(log_(sqrt(ab))abc) has the value equal to

Prove that |{:(1,,ab,,(1)/(a)+(1)/(b)),(1 ,,bc,,(1)/(b)+(1)/(c)),( 1,, ca,,(1)/(c)+(1)/(a)):}|=0

Knowledge Check

  • let a,b,c be in an A.P. consider the following statements: I. (1)/(ab),(1)/(ca),(1)/(bc) are in an A.P. II. (1)/(sqrt(b)+sqrt(c)),(1)/(sqrt(c)+sqrt(a)),(1)/(sqrt(a)+sqrt(b)) are in A.P.

    A
    A. Only I
    B
    B. Only II
    C
    C. Both I and II
    D
    D. Neither I nor II

  • Let a, b, c be in AP. Consider the following statements: 1. (1)/(ab),(1)/(ca)" and "(1)/(bc)" are in AP." 2. (1)/(sqrt(b)+sqrt(c)),(1)/(sqrt(c)+sqrt(a))" and "(1)/(sqrt(a)+sqrt(b))" are in AP." Which of the statements given above is/are correct?

    A
    1 only
    B
    2 only
    C
    Both 1 and 2
    D
    Neither 1 nor 2

    • Similar Questions

    Explore conceptually related problems

    Prove [[(1)/(a),1,bc(1)/(b),1,ca(1)/(c),1,ab]]=0

    If a, b, c are in A.P., then the following are also in A.P. (i) a^(2) (b + c), b^(2) (c + a), c^(2) (a + b) (ii) a((1)/(b) + (1)/(c)), b((1)/(c) + (1)/(a)), c ((1)/(a) + (1)/(b)) (iii) (1)/(sqrt(b) + sqrt(c)),(1)/(sqrt(c) + sqrt(a)),(1)/(sqrt(a) + sqrt(b))

    If a,b,c are in A.P then (1)/(sqrt(b)-sqrt(c)),(1)/(sqrt(c)-sqrt(a)),(1)/(sqrt(a)-sqrt(b)) are in

    Prove that tan^(-1) ((1-sqrt(x))/(1+sqrt(x))) = pi/4 - tan^(-1) sqrt(x) , "where" x gt 0

    Prove that : tan^(-1) a - tan^(-1) b = cos ^(-1) [(1+ab)/(sqrt((1+a^(2))(1+b^(2))))]

    Prove that: cot^(-1)((ab+1)/(a-b))+cot^(-1)((bc+1)/(b-c))+cot^(-1)((ca+1)/(c-a))=0 .

    Home
    Profile