maths problem 01

1)x² + y² – 4 = 04 = x² + y² >= 2√(x² y²) = 2xy 1 >= xy/2當 x² = y² 時即 x² = y² = 2 時等號成立。u = (xy)/2之最_大_值是_1_, 此時x = _√2__; y = _√2_.
2)log x + log y= log (xy),40 = x + 4y >= 2√[(x)(4y)] = 4√(xy) 100 >= xy當 x = 4y 時即 x = 20 , y = 5 時等號成立。log x + log y的最_大_值是_100_; 此時x = 20__; y = _5_.


2010-09-29 19:48:10 補充：
Corr:

log x + log y的最_大_值是_log100 = 2_; 此時x = 20__; y = _5_.