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The minimum value of P=bcx +cay +abz, wh...

The minimum value of `P=bcx +cay +abz`, when `xyz=abc`, is

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`
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CENGAGE-INEQUALITIES INVOLVING MEANS -Exercise (Single)
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  3. The least value of 6tan^2varphi+54cot^2varphi+18 is 54 when A.M.geq GM...

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  4. If a b^2c^3, a^2b^3c^4,a^3b^4c^5 are in A.P. (a ,b ,c >0), then the mi...

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  5. If y=3^(x-1)+3^(-x-1) , then the least value of y is 2 6 2//3 3//2

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  6. Minimum value of (b+c)//a+(c+a)//b+(a+b)//c (for real positive numbers...

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  7. If the product of n positive numbers is n^n , then their sum is a posi...

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  8. The minimum value of P=bcx +cay +abz, when xyz=abc, is

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  9. If l ,m ,n are the three positive roots of the equation x^3-a x^2+b x-...

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  10. If positive numbers a ,b ,c are in H.P., then equation x^2-k x+2b^(101...

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  11. For x^2-(a+3)|x|=4=0 to have real solutions, the range of a is (-oo,-7...

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  12. If a ,b ,c are the sides of a triangle, then the minimum value of a/(b...

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  13. If a,b,c,d in R^(+)-{1}, then the minimum value of log(d) a+ log(c)b+l...

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  14. If a ,b ,c in R^+, t h e n(b c)/(b+c)+(a c)/(a+c)+(a b)/(a+b) is alwa...

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  15. If a ,b ,c in R^+t h e n(a+b+c)(1/a+1/b+1/c) is always geq12 geq9 lt...

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  16. If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c...

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  17. If a,b,c,in R^(+), and a,b,c, d are in H.P. then

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  18. If a,b,c,in R^(+), such that a+b+c=18, then the maximum value of a^2,b...

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  19. f(x)=((x-2)(x-1))/(x-3), forall xgt3. The minimum value of f(x) is equ...

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  20. If a gt 0, the least value of (a^3+a^2+a+1)^2 is

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