Question

Find the greatest value of `x^2y^3z^4` if `x^2+y^2+z^2=1,w h e r ex ,y ,z` are positive.

Answer 1

We have
`(2(x^2)/(2)+3(y^2)/(3)+4(z^2)/(4))/(9) ge(((x^2)/(2))^2((y^2)/(3))^3((z^2)/(4))^4)^((1)/(9))`
`rArr (1)/(9^9) ge(x^4y^6x^8)/(2^23^34^4)`
`rArr x^4y^6z^8 le (2^23^34^4)/(9^9) `
`rArr x^2y^3z^4 le 2^5xx3^(-(15)/(2))`