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  • Confused! kindly explain, Let x, y, z be positive real numbers such that x + y + z = 12 and x3y4z5=(0.1) (600)3. Then x3+y3+z3 is equal to :

 Let x, y, z be positive real numbers such that x + y + z = 12  and x3y4z5=(0.1) (600)3.  Then x3+y3+z3 is equal to :

  • Option 1)

     270

  • Option 2)

    258

  • Option 3)

    342

  • Option 4)

     216

 

Answers (1)

best_answer

As we have learned

Relation between AM, GM and HM of two positive numbers -

AM\geqslant GM\geqslant HM

- wherein

Inequality of the three given means.

 

 

 

We have weighted A.M     \geq    weighted G.M 

\Rightarrow \frac{3(x/3)+4(y/4)+5(z/5)}{12}\geq \left ( (x/3)^3(y/4)^4 (z/5)^5\right )^{1/12}

1 \geq \frac{x^3y^42^5}{3^34^45^5}^{1/12}\Rightarrow \left ( x^3y^4z^5 \right )\leq (0.1)(600)^3

But x^3y^4z^5=(0.1)(600)^3

Which means as given A.M = G.M

\Rightarrow x/3 = y/4 = z/5\Rightarrow x^3+y^3+z^3= 3^3+4^3+5^3= 216

 

 

 

 

 

 

 

 


Option 1)

 270

Option 2)

258

Option 3)

342

Option 4)

 216

Posted by

Himanshu

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