Home
Class 12
MATHS
For anyx ,y , in R^+,x y >0 . Then the ...

For any`x ,y , in R^+,x y >0` . Then the minimum value of `(2x)/(y^3)+(x^3y)/3+(4y^2)/(9x^4)` is.

Text Solution

Verified by Experts

The correct Answer is:
2
As x,y `in` R and `xy gt 0`, so x and y will be same sign.
Therefore, all the quantities `(2x)/(y^(3)), (x^(3) y)/(3), (4y^(2))/(9x^(4))` are positive
Now A.M `ge` G.M
`implies (2x)/(y^(3)) + (x^(3) y)/(3) + (4y^(2))/(9x^(4)) ge 3 (((2x)/(y^(3)))((x^(3) y)/(3))(4y^(2))/(9x^(4)))^(1//3)`
`= 3 xx (2)/(3) = 2`
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Linked comprehension type|6 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE ENGLISH|Exercise Single correct Answer|21 Videos

  • INTEGRALS

    CENGAGE ENGLISH|Exercise All Questions|764 Videos

Similar Questions

Explore conceptually related problems

If x^2+y^2=4 then find the maximum value of (x^3+y^3)/(x+y)

If x^2+y x^2=4 then find the xamimum value of (x^3+y^3)/(x+y)

If x ,y in R and x^2+y^2+x y=1, then find the minimum value of x^3y+x y^3+4.

Evaluate : (i) (2x + 3y) ( 3x +4y)

If x=4 and y=1, find the value of ((x)/(2)-(y)/(3))((x^(2))/(4)+(xy)/(6)+(y^(2))/(9)) .

If 3x+2y=12 and x y=6 , find the value of 9x^2+4y^2

Evaluate : (v) (3x - 4y) (3x + 4y) (9x^ + 16y^2)

If 2x+3y=8 and x y=2 , find the value of 4x^2+9y^2

If (4x )/(2y)=4, what is the value of (3y)/(x) ?