The minimum value of P=b c x+c a y+a b z...

The minimum value of `P=b c x+c a y+a b z ,` when `x y z=a b c` , is `a. 3abc` `b. 6abc` `c. abc` `d. 4abc`

A

3abc

B

6abc

C

abc

D

4abc

Text Solution

Verified by Experts

The correct Answer is:

A

A.M `ge` G.M
`implies (bcx + cay + abz)/(3) ge (a^(2) b^(2) c^(2) xzy)^(1//3)`
or `bcx + cay + abz ge 3xyz`
or `bcx + acy + abz ge 3 abc`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

INEQUALITIES INVOLVING MEANS
CENGAGE PUBLICATION|Exercise Multiple correct answers type|5 Videos
INEQUALITIES INVOLVING MEANS
CENGAGE PUBLICATION|Exercise Linked comprehension type|6 Videos
INEQUALITIES INVOLVING MEANS
CENGAGE PUBLICATION|Exercise Concept Application Eexercises 6.4|4 Videos
INEQUALITIES AND MODULUS
CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos
INTEGRALS
CENGAGE PUBLICATION|Exercise All Questions|762 Videos

Similar Questions

Explore conceptually related problems

Given a=x//(y-z), b=y//(z-x), and c=z//(x-y),w h e r e .x , y and z are not all zero, then the value of a b+b c+c a is a. 0 b. 1 c. -1"" d. none of these

If the foot of the perpendicular from the origin to plane is P(a ,b ,c) , the equation of the plane is a. x/a=y/b=z/c=3 b. a x+b y+c z=3 c. a x+b y+c z=a^(2)+b^2+c^2 d. a x+b y+c z=a+b+c

Let's write the value of (a + b + c) by calculation if a^3 + b^3 + c^3 = 3abc (a ne b ne c).

If a, b, c are In A.P., then show that, (a+2b-c) (2b+c-a)(c+a-b) = 4abc

Prove that |[a x-b y-c z, a y+b x, c x+a z], [a y+b x, b y-c z-a x, b z+c y],[c x+a z, b z+c y, c z-a x-b y]|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

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, c],[c ,a ,b],[b ,c ,a]|

If x/(b + c -a) = y/(c + a - b) = z/(a + b -c) , then show that (b -c) x + (c-a) y + (a -b) z = 0 .

If three positive real number a,b,c are in AP with abc =4 , then the minimum value of b is

If a + b + c = 8 and ab + bc + ca = 11 , then find the value of a^(3)+b^(3)+c^(3)-3abc

CENGAGE PUBLICATION-INEQUALITIES INVOLVING MEANS -EXERCISES (Single Correct answer type)

The minimum value of (x^(4)+y^(4)+z^(2))/(xyz) for positive real numbe...
Text Solution
|
A rod of fixed length k slides along the coordinates axes, If it meets...
Text Solution
|
The least value of 6tan^2varphi+54cot^2varphi+18 is 54 when A.M.geq GM...
Text Solution
|
If a b^2c^3, a^2b^3c^4,a^3b^4c^5 are in A.P. (a ,b ,c >0), then the mi...
Text Solution
|
If y=3^(x-1)+3^(-x-1) , then the least value of y is 2 6 2//3 3//2
Text Solution
|
Minimum value of (b+c)//a+(c+a)//b+(a+b)//c (for real positive numbers...
Text Solution
|
If the product of n positive numbers is n^n , then their sum is a posi...
Text Solution
|
The minimum value of P=b c x+c a y+a b z , when x y z=a b c , is a. 3...
Text Solution
|
If l ,m ,n are the three positive roots of the equation x^3-a x^2+b x-...
Text Solution
|
If positive numbers a ,b ,c are in H.P., then equation x^2-k x+2b^(101...
Text Solution
|
For x^2-(a+3)|x|-4=0 to have real solutions, the range of a is a)(-oo...
Text Solution
|
If a ,b ,c are the sides of a triangle, then the minimum value of a/(b...
Text Solution
|
If a,b,c,d in R^(+)-{1}, then the minimum value of log(d) a+ log(c)b+l...
Text Solution
|
If a ,b ,c in R^+, t h e n(b c)/(b+c)+(a c)/(a+c)+(a b)/(a+b) is alwa...
Text Solution
|
If a ,b ,c in R^+t h e n(a+b+c)(1/a+1/b+1/c) is always geq12 geq9 lt...
Text Solution
|
If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c...
Text Solution
|
If a ,b ,c ,d in R^+a n da ,b ,c are in H.P., then a+d > b+c a+b > c+...
Text Solution
|
If a ,b ,c ,d in R^+ such that a+b+c=18 , then the maximum value of a...
Text Solution
|
f(x)=((x-2)(x-1))/(x-3), forall xgt3. The minimum value of f(x) is equ...
Text Solution
|
If a >0, then least value of (a^3+a^2+a+1)^2 is (a)64 a^2 (b)16 a^4 ...
Text Solution
|