Câu trả lời:
a: A=1−(22√x+1−5√x4x−1+12√x−1):√x−14x+4√x+1A=1−(22x+1−5x4x−1+12x−1):x−14x+4x+1
=1−4√x−2−5√x+2√x+14x−1⋅(2√x+1)2√x−1=1−4x−2−5x+2x+14x−1⋅(2x+1)2x−1
=1−2√x+12√x−1=1−2x+12x−1
=2√x−1−2√x−12√x−1=−22√x−1=2x−1−2x−12x−1=−22x−1
b: Để A>1−2√x2A>1−2x2 thì −22√x−1−1−2√x2>0−22x−1−1−2x2>0
⇔−22√x−1+2√x−12>0⇔−22x−1+2x−12>0
⇔−4+4x−4√x+12(2√x−1)>0⇔−4+4x−4x+12(2x−1)>0
⇔(2√x−1)2−42(2√x−1)>0⇔(2x−1)2−42(2x−1)>0
⇔2√x−32√x−1>0⇔2x−32x−1>0
=>x>9/4 hoặc 0<x<1/4