Câu trả lời:
Ta có (x-y)\(^2\) ≥ 0 (x,y>0)
⇔x\(^2\)-2xy+y\(^2\)≥ 0
⇔x\(^2\)+2xy+y\(^2\)≥ 4xy
⇔(x+y)\(^2\)≥ 4xy
⇔x+y≥\(\dfrac{4xy}{x+y}\)
⇔x+y≥\(4\dfrac{xy}{x+y}\)
⇔(x+y):\(\left(\dfrac{xy}{x+y}\right)\)≥4
⇔(x+y).\(\left(\dfrac{x+y}{xy}\right)\)≥4
⇔(x+y).\(\left(\dfrac{x}{xy}+\dfrac{y}{xy}\right)\)≥4
⇔(x+y).\(\left(\dfrac{1}{y}+\dfrac{1}{x}\right)\)≥4