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If y z+z x+x y=12 ,w h e r ex ,y ,z are ...

If `y z+z x+x y=12 ,w h e r ex ,y ,z` are positive values, find the greatest value of `x y zdot`

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Verified by Experts

Using A.M `ge` G.M we have
`(xy + yz + zx)/(3) ge (x^(2) y^(2) z^(2))^(1//3)`
`implies (x)/(3) ge (x^(2) y^(2) z^(2))^(1//2)`
`implies (xyz)_("max") = ((12)/(3))^(3//2)`
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CENGAGE-INEQUALITIES INVOLVING MEANS -Examples
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  18. Prove that (b^2+c^2)/(b+c)+(c^2+a^2)/(c+a)+(a^2+b^2)/(a+b)gt a+b+c , w...

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  19. Prove that (a^8+b^8+c^8)/(a^3b^3c^3)>1/a+1/b+1/c

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  20. If a ,b ,a n dc are positive and a+b+c=6, show that (a+1//b)2+(b+1//c)...

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