Let-2x-3y-4z-9-x-y-z-gt-0-then-the-maximum-value-of-1-x-2-2-y-3-4-z-4-is-

Question Number 24469 by Tinkutara last updated on 18/Nov/17

Let 2 x + 3 y + 4 z = 9, x, y, z > 0 then

the maximum value of {(1 + x)}^{2} {(2 + y)}^{3}

{(4 + z)}^{4} is

Commented by sushmitak last updated on 18/Nov/17

AM > GM

\frac{(1 + x) \times 2 + (2 + y) \times 3 + (4 + z) \times 4}{9} ⩾ {({(1 + x)}^{2} {(2 + y)}^{3} {(4 + z)}^{4})}^{1 / 9}

\frac{24 + 9}{9} ⩾ {({(1 + x)}^{2} {(2 + y)}^{3} {(4 + z)}^{4})}^{1 / 9}

\frac{11}{3} ⩾ {({(1 + x)}^{2} {(2 + y)}^{3} {(4 + z)}^{4})}^{1 / 9}

{(\frac{11}{3})}^{9} ⩾ {(1 + x)}^{2} {(2 + y)}^{3} {(4 + z)}^{4}

Commented by Tinkutara last updated on 18/Nov/17

Thank you very much Sir!