Question

If x^2y^3=6 then find the least value of 3x+4y

Answer 1

oh no not again!!

Answer 2

just saw this yesterday, maybe the day before
AM GM comparison

Answer 3

the gimmick is to write
\[3x=\frac{3x}{2}+\frac{3x}{2}\] and
\[4y=\frac{4y}{3}+\frac{4y}{3}+\frac{4y}{3}\]

Answer 4

the arithmetic mean of those numbers is \(\frac{3x+4y}{5}\)
i will let you compute the geometric mean

Answer 5

i did the same way but was not getting the answer @ganeshie8

Answer 6

@satellite73

Answer 7

i did the same way

Answer 8

that arithmetic mean of those 5 numbers is
\[\frac{3x+4y}{5}\] right?

Answer 9

yes

Answer 10

i similarly broke it

Answer 11

the geometric mean is ?

Answer 12

can we use cauchy shwarze property here

Answer 13

oh not that complicated
compute the geometric mean

Answer 14

root6

Answer 15

i think it is 2

Answer 16

how????????????

Answer 17

\[\sqrt[5]{\frac{3x}{2}\times \frac{3x}{2}\times \frac{4y}{3}\times \frac{4y}{3}\times\frac{4y}{3}}\]

Answer 18

ok

Answer 19

thnx @satellite73

Answer 20

yw

Answer 21

ok