Find the least value of 3x + 4y if x ^ 2y ^ 3 = 6 . I know how to do it by eliminating x and differentiating . But I think there must be a solution using AM -LRB- Arithmetic mean -RRB- and GM -LRB- Geometric mean -RRB- . What do you think ?
What is the value of -LSB- math -RSB- x -LSB- / math -RSB- if -LSB- math -RSB- 5 ^ -LCB- x + 1 -RCB- = 6 ^ y -LSB- / math -RSB- and -LSB- math -RSB- 2 ^ -LCB- x + y -RCB- = 3 ^ -LCB- x - y -RCB- -LSB- / math -RSB- ?