Bài 84 trang 130 SGK giải tích 12 nâng cao, So sánh p và q, biết:...

Bài 84. So sánh p và q, biết:

(eqalign{
& a),{left( {{2 over 3}} ight)^p} > {left( {{3 over 2}} ight)^{ – q}} cr
& c),0,{25^p} < {left( {{1 over 2}} ight)^{2q}} cr} )     

(eqalign{
& b),{left( {{8 over 3}} ight)^{ – p}} < {left( {{3 over 8}} ight)^q} cr
& d),{left( {{7 over 2}} ight)^p} < {left( {{2 over 7}} ight)^{p – 2q}} cr} )                                                           

Giải

(eqalign{
& a),{left( {{2 over 3}} ight)^p} > {left( {{3 over 2}} ight)^{ – q}} Leftrightarrow {left( {{2 over 3}} ight)^p} > {left( {{2 over 3}} ight)^q} Leftrightarrow p < q,,left( { ext{ vì },,,{2 over 3} < 1} ight) cr
& b),{left( {{8 over 3}} ight)^{ – p}} < {left( {{3 over 8}} ight)^q} Leftrightarrow {left( {{3 over 8}} ight)^p} < {left( {{3 over 8}} ight)^q} Leftrightarrow p > q,,left( { ext{ vì },,{3 over 8} < 1} ight) cr
& c),,0,{25^p} < {left( {{1 over 2}} ight)^{2q}} Leftrightarrow {left( {{1 over 4}} ight)^p} < {left( {{1 over 4}} ight)^q} Leftrightarrow ,,p > q,,left( { ext{ vì },,{1 over 4} < 1} ight) cr
& d),,{left( {{7 over 2}} ight)^p} < {left( {{2 over 7}} ight)^{p – 2q}} Leftrightarrow {left( {{7 over 2}} ight)^p} < {left( {{7 over 2}} ight)^{2q – p}} Leftrightarrow p < 2q – p,,left( { ext{ vì },,{7 over 2} > 1} ight) cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Leftrightarrow 2p < 2q Leftrightarrow p < q cr} )