Home
Class 12
MATHS
Prove that (a b+x y)(a x+b y)>4a b x y(a...

Prove that `(a b+x y)(a x+b y)>4a b x y(a , b ,x ,y >0)dot`

Text Solution

Verified by Experts

Using A.M `ge` G.M we have
`(ab + xy)/(2) gt sqrt(abxy)`
`implies ax + xy gt 2 sqrt(abxy)`
similarly, ax + by `gt 2 sqrt(abxy)`
Multiplying (1) and (2) we get
`(ab + xy) (ax + by) gt 4abxy`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Exercise 6.1|8 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Exercise 6.2|6 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Comprehension|2 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

If x+y+z=0 prove that |a x b y c z c y a z b x b z c x a y|=x y z|a b cc a bb c a|

Prove that (b+x)(c+x),(v+x)(a+x),(a+x)(b+x)(b+y)(c+y),(c+x)(a+t),(a+y)(b+y)(b+z)(c+z),(c+z)(a+z),(a+z)(b+z)]|=(b-c)(c-a)(y-z)(x-y)

Knowledge Check

  • If a = (x)/(x + y) and b = (y)/( x -y) , then (ab) /( a + b) is wqual to

    A
    `(xy )/( x ^(2) + y ^(2))`
    B
    `(x ^(2) + y ^(2))/( xy)`
    C
    `(x )/(x + y)`
    D
    `((y)/( x + y)) ^(2)`

  • If A xx B = {(a,x) (a,y) (b,x) (b,y) , find B

    A
    `(x,y)`
    B
    `(a,b)`
    C
    `(b,x)`
    D
    `(b,y)`

  • If 2 x - 3y = 7 and (a + b )x - (a + b - 3) y = 4a + b have an infinite number of solutions then

    A
    ` a= 5, b = 1 `
    B
    ` a= - 5, b = 1 `
    C
    ` a = 5, b = - 1`
    D
    `a = - 5, b = - 1 `

    • Similar Questions

    Explore conceptually related problems

    (i) If tanA-tan B=x and cot B- cot A=y . Prove that cot(A-B)=1/x + 1/y . (ii) If 2 cos A = x+1/x, 2 cos B = y + 1/y , then show that 2 cos (A-B)= x/y+y/x .

    If x ,\ y , z are not all zero and if a x+b y+c z=0; b x+c y+a z=0; c x+a y+b z=0 Prove that x : y : z=1:1:1\ or\ 1:omega:omega^2or\ 1:omega^2:omegadot

    Given that x , y a n d b are real numbers and x >0 then x/b y/b d. x/bgeqy/b

    If a = (x)/( x + y) and b = ( y)/( x - y) , then (ab)/( a + b) equals to

    If A xx B = {(a,x) (a,y)(b,x) (b,y), find A.

    Home
    Profile